यदि \(x=\sqrt{14}+\sqrt{6}\) है तो \(x^2-20\) का मान क्या है?
If \(x=\sqrt{14}+\sqrt{6}\), what is the value of \(x^2-20\)?
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A \(\sqrt{84}\)
B \(2\sqrt{84}\)
C (20)
D (84)
Explanation opens after your attempt
Correct Answer
B. \(2\sqrt{84}\)
Step 1
Concept
\(x^2=14+6+2\sqrt{84}=20+2\sqrt{84}\). So \(x^2-20=2\sqrt{84}\).
Step 2
Why this answer is correct
The correct answer is B. \(2\sqrt{84}\). \(x^2=14+6+2\sqrt{84}=20+2\sqrt{84}\). So \(x^2-20=2\sqrt{84}\).
Step 3
Exam Tip
\(x^2=14+6+2\sqrt{84}=20+2\sqrt{84}\) है। इसलिए \(x^2-20=2\sqrt{84}\) है।
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\(\frac{\sqrt{11}+\sqrt{6}}{\sqrt{11}-\sqrt{6}}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\frac{\sqrt{11}+\sqrt{6}}{\sqrt{11}-\sqrt{6}}\)?
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A \(\frac{17+2\sqrt{66}}{5}\)
B \(\frac{17-2\sqrt{66}}{5}\)
C \(17+2\sqrt{66}\)
D (5)
Explanation opens after your attempt
Correct Answer
A. \(\frac{17+2\sqrt{66}}{5}\)
Step 1
Concept
Multiplying by the conjugate gives numerator \(17+2\sqrt{66}\) and denominator (5). Rationalise the denominator and simplify.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{17+2\sqrt{66}}{5}\). Multiplying by the conjugate gives numerator \(17+2\sqrt{66}\) and denominator (5). Rationalise the denominator and simplify.
Step 3
Exam Tip
संयुग्मी से गुणा करने पर अंश \(17+2\sqrt{66}\) और हर (5) मिलता है। हर को परिमेय बनाकर सरल करें।
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यदि \(a=7+\sqrt{2}\) और \(b=7-\sqrt{2}\) हैं तो \(a^2-b^2\) का मान क्या है?
If \(a=7+\sqrt{2}\) and \(b=7-\sqrt{2}\), what is the value of \(a^2-b^2\)?
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A \(14\sqrt{2}\)
B \(28\sqrt{2}\)
C (47)
D (98)
Explanation opens after your attempt
Correct Answer
B. \(28\sqrt{2}\)
Step 1
Concept
\(a-b=2\sqrt{2}\) and (a+b=14). Therefore \(a^2-b^2=28\sqrt{2}\).
Step 2
Why this answer is correct
The correct answer is B. \(28\sqrt{2}\). \(a-b=2\sqrt{2}\) and (a+b=14). Therefore \(a^2-b^2=28\sqrt{2}\).
Step 3
Exam Tip
\(a-b=2\sqrt{2}\) और (a+b=14) है। इसलिए \(a^2-b^2=28\sqrt{2}\) है।
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\(\sqrt{605}-\sqrt{320}+\sqrt{125}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{605}-\sqrt{320}+\sqrt{125}\)?
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A \(7\sqrt{5}\)
B \(8\sqrt{5}\)
C \(9\sqrt{5}\)
D \(11\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
B. \(8\sqrt{5}\)
Step 1
Concept
\(\sqrt{605}=11\sqrt{5}\), \(\sqrt{320}=8\sqrt{5}\), and \(\sqrt{125}=5\sqrt{5}\). Therefore the result is \(8\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is B. \(8\sqrt{5}\). \(\sqrt{605}=11\sqrt{5}\), \(\sqrt{320}=8\sqrt{5}\), and \(\sqrt{125}=5\sqrt{5}\). Therefore the result is \(8\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{605}=11\sqrt{5}\), \(\sqrt{320}=8\sqrt{5}\) और \(\sqrt{125}=5\sqrt{5}\) है। इसलिए परिणाम \(8\sqrt{5}\) है।
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यदि \(p=\frac{1}{\sqrt{23}+4}\) है तो (p) का सरल रूप क्या है?
If \(p=\frac{1}{\sqrt{23}+4}\), what is the simplified form of (p)?
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A \(\frac{\sqrt{23}-4}{7}\)
B \(\sqrt{23}-4\)
C \(\frac{\sqrt{23}+4}{7}\)
D \(4-\sqrt{23}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\sqrt{23}-4}{7}\)
Step 1
Concept
Multiplying by the conjugate makes the denominator (23-16=7). So \(p=\frac{\sqrt{23}-4}{7}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\sqrt{23}-4}{7}\). Multiplying by the conjugate makes the denominator (23-16=7). So \(p=\frac{\sqrt{23}-4}{7}\).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर हर (23-16=7) बनता है। इसलिए \(p=\frac{\sqrt{23}-4}{7}\) है।
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यदि \(y=\sqrt{20}+\sqrt{45}+\sqrt{80}\) है तो \(y^2\) का मान क्या है?
If \(y=\sqrt{20}+\sqrt{45}+\sqrt{80}\), what is the value of \(y^2\)?
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A (405)
B (245)
C (225)
D \(81\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\). So \(y=9\sqrt{5}\) and \(y^2=405\).
Step 2
Why this answer is correct
The correct answer is A. (405). \(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\), and \(\sqrt{80}=4\sqrt{5}\). So \(y=9\sqrt{5}\) and \(y^2=405\).
Step 3
Exam Tip
\(\sqrt{20}=2\sqrt{5}\), \(\sqrt{45}=3\sqrt{5}\) और \(\sqrt{80}=4\sqrt{5}\) है। इसलिए \(y=9\sqrt{5}\) और \(y^2=405\) है।
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\(\frac{7}{\sqrt{30}-\sqrt{23}}\) का परिमेयकृत रूप कौन-सा है?
Which is the rationalised form of \(\frac{7}{\sqrt{30}-\sqrt{23}}\)?
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A \(\frac{\sqrt{30}+\sqrt{23}}{7}\)
B (7\(\sqrt{30}+\sqrt{23}\))
C \(\sqrt{30}+\sqrt{23}\)
D \(7\sqrt{690}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{30}+\sqrt{23}\)
Step 1
Concept
Multiplying by the conjugate makes the denominator (30-23=7). So the answer is \(\sqrt{30}+\sqrt{23}\).
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{30}+\sqrt{23}\). Multiplying by the conjugate makes the denominator (30-23=7). So the answer is \(\sqrt{30}+\sqrt{23}\).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर हर (30-23=7) बनता है। इसलिए उत्तर \(\sqrt{30}+\sqrt{23}\) है।
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यदि \(s=\sqrt{242}+\sqrt{128}\) है तो \(\frac{s}{\sqrt{2}}\) का मान क्या है?
If \(s=\sqrt{242}+\sqrt{128}\), what is the value of \(\frac{s}{\sqrt{2}}\)?
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A (17)
B (19)
C (21)
D (23)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{242}=11\sqrt{2}\) and \(\sqrt{128}=8\sqrt{2}\), so \(s=19\sqrt{2}\). Dividing gives (19).
Step 2
Why this answer is correct
The correct answer is B. (19). \(\sqrt{242}=11\sqrt{2}\) and \(\sqrt{128}=8\sqrt{2}\), so \(s=19\sqrt{2}\). Dividing gives (19).
Step 3
Exam Tip
\(\sqrt{242}=11\sqrt{2}\) और \(\sqrt{128}=8\sqrt{2}\), इसलिए \(s=19\sqrt{2}\) है। भाग देने पर (19) मिलता है।
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\(\sqrt{15+\sqrt{26}}\times\sqrt{15+\sqrt{26}}\) का मान क्या है?
What is the value of \(\sqrt{15+\sqrt{26}}\times\sqrt{15+\sqrt{26}}\)?
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A (225+26)
B \(\sqrt{41}\)
C \(15+\sqrt{26}\)
D \(15-\sqrt{26}\)
Explanation opens after your attempt
Correct Answer
C. \(15+\sqrt{26}\)
Step 1
Concept
Multiplying the same square root by itself gives the number inside. Therefore the value is \(15+\sqrt{26}\).
Step 2
Why this answer is correct
The correct answer is C. \(15+\sqrt{26}\). Multiplying the same square root by itself gives the number inside. Therefore the value is \(15+\sqrt{26}\).
Step 3
Exam Tip
एक ही वर्गमूल को अपने आप से गुणा करने पर अंदर की संख्या मिलती है। इसलिए मान \(15+\sqrt{26}\) है।
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यदि \(A=\sqrt{300}+\sqrt{108}\) और \(B=16\sqrt{3}\) हैं तो कौन-सा कथन सही है?
If \(A=\sqrt{300}+\sqrt{108}\) and \(B=16\sqrt{3}\), which statement is correct?
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A (A>B)
B (A=B)
C (A<B)
D दोनों परिमेय हैं / Both are rational
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{300}=10\sqrt{3}\) and \(\sqrt{108}=6\sqrt{3}\), so \(A=16\sqrt{3}\). Hence (A=B).
Step 2
Why this answer is correct
The correct answer is B. (A=B). \(\sqrt{300}=10\sqrt{3}\) and \(\sqrt{108}=6\sqrt{3}\), so \(A=16\sqrt{3}\). Hence (A=B).
Step 3
Exam Tip
\(\sqrt{300}=10\sqrt{3}\) और \(\sqrt{108}=6\sqrt{3}\), इसलिए \(A=16\sqrt{3}\) है। अतः (A=B) है।
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\(\frac{\sqrt{17}+\sqrt{5}}{\sqrt{17}-\sqrt{5}}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\frac{\sqrt{17}+\sqrt{5}}{\sqrt{17}-\sqrt{5}}\)?
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A \(\frac{11+\sqrt{85}}{6}\)
B \(\frac{22+2\sqrt{85}}{12}\)
C \(22+2\sqrt{85}\)
D \(\frac{11-\sqrt{85}}{6}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{11+\sqrt{85}}{6}\)
Step 1
Concept
Multiplying by the conjugate gives numerator \(22+2\sqrt{85}\) and denominator (12). The simplified form is \(\frac{11+\sqrt{85}}{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{11+\sqrt{85}}{6}\). Multiplying by the conjugate gives numerator \(22+2\sqrt{85}\) and denominator (12). The simplified form is \(\frac{11+\sqrt{85}}{6}\).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर अंश \(22+2\sqrt{85}\) और हर (12) मिलता है। सरल रूप \(\frac{11+\sqrt{85}}{6}\) है।
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यदि \(q=\sqrt{11}+3\) है तो \(q^2-6q\) का मान क्या है?
If \(q=\sqrt{11}+3\), what is the value of \(q^2-6q\)?
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A (2)
B (-2)
C (11)
D \(6\sqrt{11}\)
Explanation opens after your attempt
Step 1
Concept
\(q^2=20+6\sqrt{11}\) and \(6q=18+6\sqrt{11}\). Subtracting gives (2).
Step 2
Why this answer is correct
The correct answer is A. (2). \(q^2=20+6\sqrt{11}\) and \(6q=18+6\sqrt{11}\). Subtracting gives (2).
Step 3
Exam Tip
\(q^2=20+6\sqrt{11}\) और \(6q=18+6\sqrt{11}\) है। घटाने पर (2) मिलता है।
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(\(\sqrt{11}+\sqrt{7}\)2 -\(\sqrt{11}-\sqrt{7}\)2 ) का मान क्या है?
What is the value of (\(\sqrt{11}+\sqrt{7}\)2 -\(\sqrt{11}-\sqrt{7}\)2 )?
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A \(4\sqrt{77}\)
B (18)
C \(2\sqrt{77}\)
D (77)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{77}\)
Step 1
Concept
Use ((a+b)2 -(a-b)2 =4ab). Here the value is \(4\sqrt{77}\).
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{77}\). Use ((a+b)2 -(a-b)2 =4ab). Here the value is \(4\sqrt{77}\).
Step 3
Exam Tip
पहचान ((a+b)2 -(a-b)2 =4ab) लगाएं। यहाँ मान \(4\sqrt{77}\) है।
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यदि \(t=\sqrt{31}+5\) है तो \(t+\frac{6}{t}\) का मान क्या है?
If \(t=\sqrt{31}+5\), what is the value of \(t+\frac{6}{t}\)?
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A \(2\sqrt{31}\)
B (10)
C \(\sqrt{31}\)
D \(2\sqrt{31}+10\)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{31}\)
Step 1
Concept
\(\frac{6}{\sqrt{31}+5}=\sqrt{31}-5\) because the denominator becomes (31-25=6). So the sum is \(2\sqrt{31}\).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{31}\). \(\frac{6}{\sqrt{31}+5}=\sqrt{31}-5\) because the denominator becomes (31-25=6). So the sum is \(2\sqrt{31}\).
Step 3
Exam Tip
\(\frac{6}{\sqrt{31}+5}=\sqrt{31}-5\) है क्योंकि हर (31-25=6) बनता है। इसलिए योग \(2\sqrt{31}\) है।
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\(\frac{\sqrt{300}-\sqrt{108}}{\sqrt{3}}\) का मान क्या है?
What is the value of \(\frac{\sqrt{300}-\sqrt{108}}{\sqrt{3}}\)?
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{300}=10\sqrt{3}\) and \(\sqrt{108}=6\sqrt{3}\), so the numerator is \(4\sqrt{3}\). Dividing gives (4).
Step 2
Why this answer is correct
The correct answer is B. (4). \(\sqrt{300}=10\sqrt{3}\) and \(\sqrt{108}=6\sqrt{3}\), so the numerator is \(4\sqrt{3}\). Dividing gives (4).
Step 3
Exam Tip
\(\sqrt{300}=10\sqrt{3}\) और \(\sqrt{108}=6\sqrt{3}\), इसलिए अंश \(4\sqrt{3}\) है। भाग देने पर (4) मिलता है।
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यदि \(c=\sqrt{26}+\sqrt{10}\) और \(d=\sqrt{26}-\sqrt{10}\) हैं तो (cd) और (c-d) का सही युग्म कौन-सा है?
If \(c=\sqrt{26}+\sqrt{10}\) and \(d=\sqrt{26}-\sqrt{10}\), which is the correct pair of (cd) and (c-d)?
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A (16), \(2\sqrt{10}\)
B (36), \(2\sqrt{26}\)
C \(16\sqrt{260}\), \(2\sqrt{10}\)
D (26), (10)
Explanation opens after your attempt
Correct Answer
A. (16), \(2\sqrt{10}\)
Step 1
Concept
(cd=26-10=16) and \(c-d=2\sqrt{10}\). Find both values separately in a conjugate pair.
Step 2
Why this answer is correct
The correct answer is A. (16), \(2\sqrt{10}\). (cd=26-10=16) and \(c-d=2\sqrt{10}\). Find both values separately in a conjugate pair.
Step 3
Exam Tip
(cd=26-10=16) और \(c-d=2\sqrt{10}\) है। संयुग्मी युग्म में दोनों मान अलग-अलग निकालें।
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\(\sqrt{847}-\sqrt{363}+\sqrt{147}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{847}-\sqrt{363}+\sqrt{147}\)?
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A \(7\sqrt{7}\)
B \(9\sqrt{7}\)
C \(11\sqrt{7}\)
D \(13\sqrt{7}\)
Explanation opens after your attempt
Correct Answer
B. \(9\sqrt{7}\)
Step 1
Concept
\(\sqrt{847}=11\sqrt{7}\), \(\sqrt{363}=7\sqrt{7}\), and \(\sqrt{147}=3\sqrt{7}\). So the result is \(11\sqrt{7}-7\sqrt{7}+3\sqrt{7}=7\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is B. \(9\sqrt{7}\). \(\sqrt{847}=11\sqrt{7}\), \(\sqrt{363}=7\sqrt{7}\), and \(\sqrt{147}=3\sqrt{7}\). So the result is \(11\sqrt{7}-7\sqrt{7}+3\sqrt{7}=7\sqrt{7}\).
Step 3
Exam Tip
\(\sqrt{847}=11\sqrt{7}\), \(\sqrt{363}=7\sqrt{7}\) और \(\sqrt{147}=3\sqrt{7}\) है। इसलिए परिणाम \(7\sqrt{7}\) नहीं, \(11\sqrt{7}-7\sqrt{7}+3\sqrt{7}=7\sqrt{7}\) है।
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\(\frac{8}{\sqrt{27}-\sqrt{11}}\) का परिमेयकृत रूप क्या है?
What is the rationalised form of \(\frac{8}{\sqrt{27}-\sqrt{11}}\)?
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A \(\sqrt{27}+\sqrt{11}\)
B \(\frac{\sqrt{27}+\sqrt{11}}{2}\)
C (\frac{8\(\sqrt{27}+\sqrt{11}\)}{16})
D \(8\sqrt{297}\)
Explanation opens after your attempt
Correct Answer
C. (\frac{8\(\sqrt{27}+\sqrt{11}\)}{16})
Step 1
Concept
Multiplying by the conjugate makes the denominator (27-11=16). So the form is (\frac{8\(\sqrt{27}+\sqrt{11}\)}{16}).
Step 2
Why this answer is correct
The correct answer is C. (\frac{8\(\sqrt{27}+\sqrt{11}\)}{16}). Multiplying by the conjugate makes the denominator (27-11=16). So the form is (\frac{8\(\sqrt{27}+\sqrt{11}\)}{16}).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर हर (27-11=16) बनता है। इसलिए रूप (\frac{8\(\sqrt{27}+\sqrt{11}\)}{16}) है।
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यदि \(x=\sqrt{21}+\sqrt{8}\) है तो \(x^2-29\) का मान क्या है?
If \(x=\sqrt{21}+\sqrt{8}\), what is the value of \(x^2-29\)?
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A \(\sqrt{168}\)
B (29)
C \(2\sqrt{168}\)
D (168)
Explanation opens after your attempt
Correct Answer
C. \(2\sqrt{168}\)
Step 1
Concept
\(x^2=21+8+2\sqrt{168}=29+2\sqrt{168}\). So \(x^2-29=2\sqrt{168}\).
Step 2
Why this answer is correct
The correct answer is C. \(2\sqrt{168}\). \(x^2=21+8+2\sqrt{168}=29+2\sqrt{168}\). So \(x^2-29=2\sqrt{168}\).
Step 3
Exam Tip
\(x^2=21+8+2\sqrt{168}=29+2\sqrt{168}\) है। इसलिए \(x^2-29=2\sqrt{168}\) है।
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\(\sqrt{16+\sqrt{45}}\) का वर्ग किसके बराबर है?
What is the square of \(\sqrt{16+\sqrt{45}}\) equal to?
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A \(16-\sqrt{45}\)
B \(\sqrt{61}\)
C (256+45)
D \(16+\sqrt{45}\)
Explanation opens after your attempt
Correct Answer
D. \(16+\sqrt{45}\)
Step 1
Concept
The square of a square root gives the number inside. So (\left\(\sqrt{16+\sqrt{45}}\right\)2 =16+\sqrt{45}).
Step 2
Why this answer is correct
The correct answer is D. \(16+\sqrt{45}\). The square of a square root gives the number inside. So (\left\(\sqrt{16+\sqrt{45}}\right\)2 =16+\sqrt{45}).
Step 3
Exam Tip
वर्गमूल का वर्ग अंदर की संख्या देता है। इसलिए (\left\(\sqrt{16+\sqrt{45}}\right\)2 =16+\sqrt{45}) है।
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यदि एक आयत की लंबाई \(\sqrt{30}+\sqrt{11}\) और चौड़ाई \(\sqrt{30}-\sqrt{11}\) है तो क्षेत्रफल क्या होगा?
If a rectangle has length \(\sqrt{30}+\sqrt{11}\) and breadth \(\sqrt{30}-\sqrt{11}\), what will be its area?
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A (41)
B (19)
C \(\sqrt{330}\)
D \(2\sqrt{30}\)
Explanation opens after your attempt
Step 1
Concept
Area is (\(\sqrt{30}+\sqrt{11}\)\(\sqrt{30}-\sqrt{11}\)=30-11=19). Conjugate dimensions give rational area.
Step 2
Why this answer is correct
The correct answer is B. (19). Area is (\(\sqrt{30}+\sqrt{11}\)\(\sqrt{30}-\sqrt{11}\)=30-11=19). Conjugate dimensions give rational area.
Step 3
Exam Tip
क्षेत्रफल (\(\sqrt{30}+\sqrt{11}\)\(\sqrt{30}-\sqrt{11}\)=30-11=19) है। संयुग्मी आयामों से परिमेय क्षेत्रफल मिलता है।
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(\(\sqrt{112}+\sqrt{63}\)\(\sqrt{112}-\sqrt{63}\)) का मान क्या है?
What is the value of (\(\sqrt{112}+\sqrt{63}\)\(\sqrt{112}-\sqrt{63}\))?
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A (175)
B \(2\sqrt{7056}\)
C (49)
D (-49)
Explanation opens after your attempt
Step 1
Concept
This is the \(a^2-b^2\) form. So the value is (112-63=49).
Step 2
Why this answer is correct
The correct answer is C. (49). This is the \(a^2-b^2\) form. So the value is (112-63=49).
Step 3
Exam Tip
यह \(a^2-b^2\) रूप है। इसलिए मान (112-63=49) है।
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यदि \(y=\sqrt{75}+\sqrt{147}\) है तो \(\frac{y}{\sqrt{3}}\) का मान क्या है?
If \(y=\sqrt{75}+\sqrt{147}\), what is the value of \(\frac{y}{\sqrt{3}}\)?
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A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{147}=7\sqrt{3}\), so \(y=12\sqrt{3}\). Dividing gives (12).
Step 2
Why this answer is correct
The correct answer is B. (12). \(\sqrt{75}=5\sqrt{3}\) and \(\sqrt{147}=7\sqrt{3}\), so \(y=12\sqrt{3}\). Dividing gives (12).
Step 3
Exam Tip
\(\sqrt{75}=5\sqrt{3}\) और \(\sqrt{147}=7\sqrt{3}\), इसलिए \(y=12\sqrt{3}\) है। भाग देने पर (12) मिलता है।
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\(\frac{\sqrt{10}-\sqrt{6}}{\sqrt{10}+\sqrt{6}}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\frac{\sqrt{10}-\sqrt{6}}{\sqrt{10}+\sqrt{6}}\)?
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A \(4+\sqrt{15}\)
B (1)
C \(4-\sqrt{15}\)
D \(\sqrt{15}-4\)
Explanation opens after your attempt
Correct Answer
C. \(4-\sqrt{15}\)
Step 1
Concept
Multiplying by the conjugate gives (\frac{\(\sqrt{10}-\sqrt{6}\)2 }{4}=4-\sqrt{15}). Make the denominator rational.
Step 2
Why this answer is correct
The correct answer is C. \(4-\sqrt{15}\). Multiplying by the conjugate gives (\frac{\(\sqrt{10}-\sqrt{6}\)2 }{4}=4-\sqrt{15}). Make the denominator rational.
Step 3
Exam Tip
संयुग्मी से गुणा करने पर (\frac{\(\sqrt{10}-\sqrt{6}\)2 }{4}=4-\sqrt{15}) मिलता है। हर को परिमेय बनाएं।
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यदि \(m=\sqrt{245}-\sqrt{125}\) और \(n=2\sqrt{5}\) हैं तो (m-n) क्या है?
If \(m=\sqrt{245}-\sqrt{125}\) and \(n=2\sqrt{5}\), what is (m-n)?
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A (0)
B \(\sqrt{5}\)
C \(4\sqrt{5}\)
D \(6\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{245}=7\sqrt{5}\) and \(\sqrt{125}=5\sqrt{5}\), so \(m=2\sqrt{5}\). Hence (m-n=0).
Step 2
Why this answer is correct
The correct answer is A. (0). \(\sqrt{245}=7\sqrt{5}\) and \(\sqrt{125}=5\sqrt{5}\), so \(m=2\sqrt{5}\). Hence (m-n=0).
Step 3
Exam Tip
\(\sqrt{245}=7\sqrt{5}\) और \(\sqrt{125}=5\sqrt{5}\), इसलिए \(m=2\sqrt{5}\) है। अतः (m-n=0) है।
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(\sqrt{11}\left\(\sqrt{539}-\sqrt{275}\right\)) का मान क्या है?
What is the value of (\sqrt{11}\left\(\sqrt{539}-\sqrt{275}\right\))?
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A \(2\sqrt{11}\)
B (22)
C (44)
D \(\sqrt{484}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{539}=7\sqrt{11}\) and \(\sqrt{275}=5\sqrt{11}\), so the bracket is \(2\sqrt{11}\). Multiplying by \(\sqrt{11}\) gives (22).
Step 2
Why this answer is correct
The correct answer is B. (22). \(\sqrt{539}=7\sqrt{11}\) and \(\sqrt{275}=5\sqrt{11}\), so the bracket is \(2\sqrt{11}\). Multiplying by \(\sqrt{11}\) gives (22).
Step 3
Exam Tip
\(\sqrt{539}=7\sqrt{11}\) और \(\sqrt{275}=5\sqrt{11}\), इसलिए कोष्ठक \(2\sqrt{11}\) है। \(\sqrt{11}\) से गुणा करने पर (22) मिलता है।
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यदि \(z=\sqrt{29}-\sqrt{18}\) है तो \(z^2\) का मान कौन-सा है?
If \(z=\sqrt{29}-\sqrt{18}\), which is the value of \(z^2\)?
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A \(47+2\sqrt{522}\)
B (11)
C \(47-2\sqrt{522}\)
D \(\sqrt{11}\)
Explanation opens after your attempt
Correct Answer
C. \(47-2\sqrt{522}\)
Step 1
Concept
(\(\sqrt{29}-\sqrt{18}\)2 =29+18-2\sqrt{522}). Keep the middle term negative.
Step 2
Why this answer is correct
The correct answer is C. \(47-2\sqrt{522}\). (\(\sqrt{29}-\sqrt{18}\)2 =29+18-2\sqrt{522}). Keep the middle term negative.
Step 3
Exam Tip
(\(\sqrt{29}-\sqrt{18}\)2 =29+18-2\sqrt{522}) है। मध्य पद का चिन्ह ऋणात्मक रखें।
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\(\frac{5}{\sqrt{26}+\sqrt{17}}\) का परिमेयकृत रूप क्या है?
What is the rationalised form of \(\frac{5}{\sqrt{26}+\sqrt{17}}\)?
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A \(\sqrt{26}-\sqrt{17}\)
B \(\sqrt{26}+\sqrt{17}\)
C (\frac{5\(\sqrt{26}-\sqrt{17}\)}{9})
D \(5\sqrt{442}\)
Explanation opens after your attempt
Correct Answer
C. (\frac{5\(\sqrt{26}-\sqrt{17}\)}{9})
Step 1
Concept
Multiplying by the conjugate makes the denominator (26-17=9). So the form is (\frac{5\(\sqrt{26}-\sqrt{17}\)}{9}).
Step 2
Why this answer is correct
The correct answer is C. (\frac{5\(\sqrt{26}-\sqrt{17}\)}{9}). Multiplying by the conjugate makes the denominator (26-17=9). So the form is (\frac{5\(\sqrt{26}-\sqrt{17}\)}{9}).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर हर (26-17=9) बनता है। इसलिए रूप (\frac{5\(\sqrt{26}-\sqrt{17}\)}{9}) है।
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यदि \(x=\sqrt{5}+\sqrt{45}\) और \(y=\sqrt{80}\) हैं तो (x-y) का मान क्या है?
If \(x=\sqrt{5}+\sqrt{45}\) and \(y=\sqrt{80}\), what is the value of (x-y)?
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A (0)
B \(\sqrt{5}\)
C \(2\sqrt{5}\)
D \(4\sqrt{5}\)
Explanation opens after your attempt
Step 1
Concept
\(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\) and \(y=4\sqrt{5}\). Therefore (x-y=0).
Step 2
Why this answer is correct
The correct answer is A. (0). \(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\) and \(y=4\sqrt{5}\). Therefore (x-y=0).
Step 3
Exam Tip
\(x=\sqrt{5}+3\sqrt{5}=4\sqrt{5}\) और \(y=4\sqrt{5}\) है। इसलिए (x-y=0) है।
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\(\sqrt{26}\) और \(\sqrt{30}\) के बीच कौन-सी संख्या निश्चित रूप से आती है?
Which number definitely lies between \(\sqrt{26}\) and \(\sqrt{30}\)?
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A \(\sqrt{25}\)
B (6)
C \(\sqrt{28}\)
D \(\sqrt{31}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{28}\)
Step 1
Concept
Since (26<28<30), \(\sqrt{28}\) lies between them. Compare square roots using the numbers inside.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{28}\). Since (26<28<30), \(\sqrt{28}\) lies between them. Compare square roots using the numbers inside.
Step 3
Exam Tip
क्योंकि (26<28<30), इसलिए \(\sqrt{28}\) दोनों के बीच होगा। वर्गमूलों में अंदर की संख्या से तुलना करें।
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यदि \(u=\sqrt{112}+\sqrt{175}\) और \(v=9\sqrt{7}\) हैं तो कौन-सा कथन सही है?
If \(u=\sqrt{112}+\sqrt{175}\) and \(v=9\sqrt{7}\), which statement is correct?
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A (u>v)
B (u<v)
C (u=v)
D दोनों परिमेय हैं / Both are rational
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{112}=4\sqrt{7}\) and \(\sqrt{175}=5\sqrt{7}\), so \(u=9\sqrt{7}\). Hence (u=v).
Step 2
Why this answer is correct
The correct answer is C. (u=v). \(\sqrt{112}=4\sqrt{7}\) and \(\sqrt{175}=5\sqrt{7}\), so \(u=9\sqrt{7}\). Hence (u=v).
Step 3
Exam Tip
\(\sqrt{112}=4\sqrt{7}\) और \(\sqrt{175}=5\sqrt{7}\), इसलिए \(u=9\sqrt{7}\) है। अतः (u=v) है।
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(\(\sqrt{23}+5\)2 -\(\sqrt{23}-5\)2 ) का मान क्या है?
What is the value of (\(\sqrt{23}+5\)2 -\(\sqrt{23}-5\)2 )?
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A \(10\sqrt{23}\)
B (28)
C \(20\sqrt{23}\)
D (92)
Explanation opens after your attempt
Correct Answer
C. \(20\sqrt{23}\)
Step 1
Concept
Use ((a+b)2 -(a-b)2 =4ab). Here \(a=\sqrt{23}\) and (b=5), so the value is \(20\sqrt{23}\).
Step 2
Why this answer is correct
The correct answer is C. \(20\sqrt{23}\). Use ((a+b)2 -(a-b)2 =4ab). Here \(a=\sqrt{23}\) and (b=5), so the value is \(20\sqrt{23}\).
Step 3
Exam Tip
पहचान ((a+b)2 -(a-b)2 =4ab) लगाएं। यहाँ \(a=\sqrt{23}\) और (b=5), इसलिए मान \(20\sqrt{23}\) है।
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यदि \(x=6+\sqrt{35}\) है तो \(x^2-12x\) का मान क्या है?
If \(x=6+\sqrt{35}\), what is the value of \(x^2-12x\)?
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A (-1)
B (1)
C (35)
D \(2\sqrt{35}\)
Explanation opens after your attempt
Step 1
Concept
\(x^2=71+12\sqrt{35}\) and \(12x=72+12\sqrt{35}\). Subtracting gives (-1).
Step 2
Why this answer is correct
The correct answer is A. (-1). \(x^2=71+12\sqrt{35}\) and \(12x=72+12\sqrt{35}\). Subtracting gives (-1).
Step 3
Exam Tip
\(x^2=71+12\sqrt{35}\) और \(12x=72+12\sqrt{35}\) है। घटाने पर (-1) मिलता है।
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\(\sqrt{588}-\sqrt{300}+\sqrt{192}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{588}-\sqrt{300}+\sqrt{192}\)?
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A \(8\sqrt{3}\)
B \(10\sqrt{3}\)
C \(12\sqrt{3}\)
D \(\sqrt{480}\)
Explanation opens after your attempt
Correct Answer
C. \(12\sqrt{3}\)
Step 1
Concept
\(\sqrt{588}=14\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), and \(\sqrt{192}=8\sqrt{3}\). Therefore the result is \(12\sqrt{3}\).
Step 2
Why this answer is correct
The correct answer is C. \(12\sqrt{3}\). \(\sqrt{588}=14\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\), and \(\sqrt{192}=8\sqrt{3}\). Therefore the result is \(12\sqrt{3}\).
Step 3
Exam Tip
\(\sqrt{588}=14\sqrt{3}\), \(\sqrt{300}=10\sqrt{3}\) और \(\sqrt{192}=8\sqrt{3}\) है। इसलिए परिणाम \(12\sqrt{3}\) है।
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\(\frac{1}{\sqrt{10}+\sqrt{6}}+\frac{1}{\sqrt{10}-\sqrt{6}}\) का मान क्या है?
What is the value of \(\frac{1}{\sqrt{10}+\sqrt{6}}+\frac{1}{\sqrt{10}-\sqrt{6}}\)?
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A \(\frac{\sqrt{10}}{2}\)
B \(\sqrt{6}\)
C \(2\sqrt{10}\)
D (4)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\sqrt{10}}{2}\)
Step 1
Concept
Adding the two terms gives numerator \(2\sqrt{10}\) and denominator (10-6=4). So the value is \(\frac{\sqrt{10}}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\sqrt{10}}{2}\). Adding the two terms gives numerator \(2\sqrt{10}\) and denominator (10-6=4). So the value is \(\frac{\sqrt{10}}{2}\).
Step 3
Exam Tip
दोनों पदों को जोड़ने पर अंश \(2\sqrt{10}\) और हर (10-6=4) मिलता है। इसलिए मान \(\frac{\sqrt{10}}{2}\) है।
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यदि \(x=\sqrt{17+\sqrt{13}}\) है तो \(x^2-17\) का मान क्या है?
If \(x=\sqrt{17+\sqrt{13}}\), what is the value of \(x^2-17\)?
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A \(\sqrt{13}\)
B (13)
C \(\sqrt{30}\)
D (17)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{13}\)
Step 1
Concept
\(x^2=17+\sqrt{13}\). Therefore \(x^2-17=\sqrt{13}\).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{13}\). \(x^2=17+\sqrt{13}\). Therefore \(x^2-17=\sqrt{13}\).
Step 3
Exam Tip
\(x^2=17+\sqrt{13}\) है। इसलिए \(x^2-17=\sqrt{13}\) होगा।
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\(\frac{\sqrt{392}+\sqrt{200}}{\sqrt{2}}\) का मान क्या है?
What is the value of \(\frac{\sqrt{392}+\sqrt{200}}{\sqrt{2}}\)?
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A (20)
B (22)
C (24)
D (26)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{392}=14\sqrt{2}\) and \(\sqrt{200}=10\sqrt{2}\), so the numerator is \(24\sqrt{2}\). Dividing gives (24).
Step 2
Why this answer is correct
The correct answer is C. (24). \(\sqrt{392}=14\sqrt{2}\) and \(\sqrt{200}=10\sqrt{2}\), so the numerator is \(24\sqrt{2}\). Dividing gives (24).
Step 3
Exam Tip
\(\sqrt{392}=14\sqrt{2}\) और \(\sqrt{200}=10\sqrt{2}\), इसलिए अंश \(24\sqrt{2}\) है। भाग देने पर (24) मिलता है।
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यदि \(r=\sqrt{17}+\sqrt{11}\) और \(s=\sqrt{17}-\sqrt{11}\) हैं तो \(r^2-s^2\) का मान क्या है?
If \(r=\sqrt{17}+\sqrt{11}\) and \(s=\sqrt{17}-\sqrt{11}\), what is the value of \(r^2-s^2\)?
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A \(4\sqrt{187}\)
B (28)
C \(2\sqrt{187}\)
D (187)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{187}\)
Step 1
Concept
(r-2 -s-2 =(r-s)(r+s)), where \(r-s=2\sqrt{11}\) and \(r+s=2\sqrt{17}\). So the value is \(4\sqrt{187}\).
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{187}\). (r-2 -s-2 =(r-s)(r+s)), where \(r-s=2\sqrt{11}\) and \(r+s=2\sqrt{17}\). So the value is \(4\sqrt{187}\).
Step 3
Exam Tip
(r-2 -s-2 =(r-s)(r+s)) है जहाँ \(r-s=2\sqrt{11}\) और \(r+s=2\sqrt{17}\) है। इसलिए मान \(4\sqrt{187}\) है।
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\(\frac{10}{\sqrt{35}-5}\) का परिमेयकृत रूप कौन-सा है?
Which is the rationalised form of \(\frac{10}{\sqrt{35}-5}\)?
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A \(\sqrt{35}+5\)
B (10\(\sqrt{35}+5\))
C \(\frac{\sqrt{35}+5}{10}\)
D \(10\sqrt{35}\)
Explanation opens after your attempt
Correct Answer
A. \(\sqrt{35}+5\)
Step 1
Concept
Multiplying by the conjugate makes the denominator (35-25=10). So the answer is \(\sqrt{35}+5\).
Step 2
Why this answer is correct
The correct answer is A. \(\sqrt{35}+5\). Multiplying by the conjugate makes the denominator (35-25=10). So the answer is \(\sqrt{35}+5\).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर हर (35-25=10) बनता है। इसलिए उत्तर \(\sqrt{35}+5\) है।
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यदि \(P=\sqrt{500}+\sqrt{180}-\sqrt{320}\) है तो (P) किसके बराबर है?
If \(P=\sqrt{500}+\sqrt{180}-\sqrt{320}\), what is (P) equal to?
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A \(6\sqrt{5}\)
B \(8\sqrt{5}\)
C \(10\sqrt{5}\)
D \(12\sqrt{5}\)
Explanation opens after your attempt
Correct Answer
B. \(8\sqrt{5}\)
Step 1
Concept
\(\sqrt{500}=10\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), and \(\sqrt{320}=8\sqrt{5}\). Therefore \(P=8\sqrt{5}\).
Step 2
Why this answer is correct
The correct answer is B. \(8\sqrt{5}\). \(\sqrt{500}=10\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\), and \(\sqrt{320}=8\sqrt{5}\). Therefore \(P=8\sqrt{5}\).
Step 3
Exam Tip
\(\sqrt{500}=10\sqrt{5}\), \(\sqrt{180}=6\sqrt{5}\) और \(\sqrt{320}=8\sqrt{5}\) है। इसलिए \(P=8\sqrt{5}\) है।
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(\(\sqrt{125}+\sqrt{320}\)2 ) का मान क्या है?
What is the value of (\(\sqrt{125}+\sqrt{320}\)2 )?
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A (845)
B (445)
C \(13\sqrt{5}\)
D (169)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{320}=8\sqrt{5}\), so the sum is \(13\sqrt{5}\). Its square is (845).
Step 2
Why this answer is correct
The correct answer is A. (845). \(\sqrt{125}=5\sqrt{5}\) and \(\sqrt{320}=8\sqrt{5}\), so the sum is \(13\sqrt{5}\). Its square is (845).
Step 3
Exam Tip
\(\sqrt{125}=5\sqrt{5}\) और \(\sqrt{320}=8\sqrt{5}\), इसलिए योग \(13\sqrt{5}\) है। इसका वर्ग (845) है।
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यदि \(w=\sqrt{18}+\sqrt{13}\) है तो \(w^2-31\) का मान क्या है?
If \(w=\sqrt{18}+\sqrt{13}\), what is the value of \(w^2-31\)?
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A \(\sqrt{234}\)
B \(2\sqrt{234}\)
C (31)
D (234)
Explanation opens after your attempt
Correct Answer
B. \(2\sqrt{234}\)
Step 1
Concept
\(w^2=18+13+2\sqrt{234}=31+2\sqrt{234}\). So \(w^2-31=2\sqrt{234}\).
Step 2
Why this answer is correct
The correct answer is B. \(2\sqrt{234}\). \(w^2=18+13+2\sqrt{234}=31+2\sqrt{234}\). So \(w^2-31=2\sqrt{234}\).
Step 3
Exam Tip
\(w^2=18+13+2\sqrt{234}=31+2\sqrt{234}\) है। इसलिए \(w^2-31=2\sqrt{234}\) है।
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यदि \(x=\sqrt{22}+\sqrt{10}\) है तो \(x^2-32\) का मान क्या है?
If \(x=\sqrt{22}+\sqrt{10}\), what is the value of \(x^2-32\)?
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A \(2\sqrt{220}\)
B \(\sqrt{220}\)
C (32)
D (220)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{220}\)
Step 1
Concept
\(x^2=22+10+2\sqrt{220}=32+2\sqrt{220}\). So \(x^2-32=2\sqrt{220}\).
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{220}\). \(x^2=22+10+2\sqrt{220}=32+2\sqrt{220}\). So \(x^2-32=2\sqrt{220}\).
Step 3
Exam Tip
\(x^2=22+10+2\sqrt{220}=32+2\sqrt{220}\) है। इसलिए \(x^2-32=2\sqrt{220}\) है।
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\(\frac{\sqrt{31}+\sqrt{19}}{\sqrt{31}-\sqrt{19}}\) का सरल रूप कौन-सा है?
Which is the simplified form of \(\frac{\sqrt{31}+\sqrt{19}}{\sqrt{31}-\sqrt{19}}\)?
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A \(\frac{25+\sqrt{589}}{6}\)
B \(\frac{25-\sqrt{589}}{6}\)
C \(50+2\sqrt{589}\)
D (12)
Explanation opens after your attempt
Correct Answer
A. \(\frac{25+\sqrt{589}}{6}\)
Step 1
Concept
Multiplying by the conjugate gives numerator \(50+2\sqrt{589}\) and denominator (12). The simplified form is \(\frac{25+\sqrt{589}}{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{25+\sqrt{589}}{6}\). Multiplying by the conjugate gives numerator \(50+2\sqrt{589}\) and denominator (12). The simplified form is \(\frac{25+\sqrt{589}}{6}\).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर अंश \(50+2\sqrt{589}\) और हर (12) मिलता है। सरल रूप \(\frac{25+\sqrt{589}}{6}\) है।
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यदि \(a=8+\sqrt{7}\) और \(b=8-\sqrt{7}\) हैं तो \(a^2-b^2\) का मान क्या है?
If \(a=8+\sqrt{7}\) and \(b=8-\sqrt{7}\), what is the value of \(a^2-b^2\)?
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A \(16\sqrt{7}\)
B \(32\sqrt{7}\)
C (57)
D (128)
Explanation opens after your attempt
Correct Answer
B. \(32\sqrt{7}\)
Step 1
Concept
\(a-b=2\sqrt{7}\) and (a+b=16). Therefore \(a^2-b^2=32\sqrt{7}\).
Step 2
Why this answer is correct
The correct answer is B. \(32\sqrt{7}\). \(a-b=2\sqrt{7}\) and (a+b=16). Therefore \(a^2-b^2=32\sqrt{7}\).
Step 3
Exam Tip
\(a-b=2\sqrt{7}\) और (a+b=16) है। इसलिए \(a^2-b^2=32\sqrt{7}\) है।
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\(\sqrt{726}-\sqrt{486}+\sqrt{150}\) का सरल रूप क्या है?
What is the simplified form of \(\sqrt{726}-\sqrt{486}+\sqrt{150}\)?
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A \(7\sqrt{6}\)
B \(9\sqrt{6}\)
C \(11\sqrt{6}\)
D \(13\sqrt{6}\)
Explanation opens after your attempt
Correct Answer
A. \(7\sqrt{6}\)
Step 1
Concept
\(\sqrt{726}=11\sqrt{6}\), \(\sqrt{486}=9\sqrt{6}\), and \(\sqrt{150}=5\sqrt{6}\). Therefore the result is \(7\sqrt{6}\).
Step 2
Why this answer is correct
The correct answer is A. \(7\sqrt{6}\). \(\sqrt{726}=11\sqrt{6}\), \(\sqrt{486}=9\sqrt{6}\), and \(\sqrt{150}=5\sqrt{6}\). Therefore the result is \(7\sqrt{6}\).
Step 3
Exam Tip
\(\sqrt{726}=11\sqrt{6}\), \(\sqrt{486}=9\sqrt{6}\) और \(\sqrt{150}=5\sqrt{6}\) है। इसलिए परिणाम \(7\sqrt{6}\) है।
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\(\frac{12}{\sqrt{43}-\sqrt{31}}\) का परिमेयकृत रूप कौन-सा है?
Which is the rationalised form of \(\frac{12}{\sqrt{43}-\sqrt{31}}\)?
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A \(\frac{\sqrt{43}+\sqrt{31}}{12}\)
B \(\sqrt{43}-\sqrt{31}\)
C \(\sqrt{43}+\sqrt{31}\)
D \(12\sqrt{1333}\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{43}+\sqrt{31}\)
Step 1
Concept
Multiplying by the conjugate makes the denominator (43-31=12). So the answer is \(\sqrt{43}+\sqrt{31}\).
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{43}+\sqrt{31}\). Multiplying by the conjugate makes the denominator (43-31=12). So the answer is \(\sqrt{43}+\sqrt{31}\).
Step 3
Exam Tip
संयुग्मी से गुणा करने पर हर (43-31=12) बनता है। इसलिए उत्तर \(\sqrt{43}+\sqrt{31}\) है।
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यदि \(q=\sqrt{15}+4\) है तो \(q^2-8q\) का मान क्या है?
If \(q=\sqrt{15}+4\), what is the value of \(q^2-8q\)?
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A (-1)
B (1)
C (15)
D \(8\sqrt{15}\)
Explanation opens after your attempt
Step 1
Concept
\(q^2=31+8\sqrt{15}\) and \(8q=32+8\sqrt{15}\). Subtracting gives (-1).
Step 2
Why this answer is correct
The correct answer is A. (-1). \(q^2=31+8\sqrt{15}\) and \(8q=32+8\sqrt{15}\). Subtracting gives (-1).
Step 3
Exam Tip
\(q^2=31+8\sqrt{15}\) और \(8q=32+8\sqrt{15}\) है। घटाने पर (-1) मिलता है।
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यदि एक आयत की लंबाई \(\sqrt{41}+\sqrt{17}\) और चौड़ाई \(\sqrt{41}-\sqrt{17}\) है तो क्षेत्रफल क्या होगा?
If a rectangle has length \(\sqrt{41}+\sqrt{17}\) and breadth \(\sqrt{41}-\sqrt{17}\), what will be its area?
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A (58)
B (24)
C \(\sqrt{697}\)
D \(2\sqrt{41}\)
Explanation opens after your attempt
Step 1
Concept
Area is (\(\sqrt{41}+\sqrt{17}\)\(\sqrt{41}-\sqrt{17}\)=41-17=24). Conjugate dimensions give rational area.
Step 2
Why this answer is correct
The correct answer is B. (24). Area is (\(\sqrt{41}+\sqrt{17}\)\(\sqrt{41}-\sqrt{17}\)=41-17=24). Conjugate dimensions give rational area.
Step 3
Exam Tip
क्षेत्रफल (\(\sqrt{41}+\sqrt{17}\)\(\sqrt{41}-\sqrt{17}\)=41-17=24) है। संयुग्मी आयामों से परिमेय क्षेत्रफल मिलता है।
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किस विकल्प में दो अपरिमेय संख्याओं का भाग परिमेय है?
In which option is the quotient of two irrational numbers rational?
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A \(\frac{\sqrt{75}}{\sqrt{3}}\)
B \(\frac{\sqrt{14}}{\sqrt{2}}\)
C \(\frac{\sqrt{30}}{\sqrt{5}}\)
D \(\frac{\sqrt{55}}{\sqrt{5}}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{\sqrt{75}}{\sqrt{3}}\)
Step 1
Concept
\(\frac{\sqrt{75}}{\sqrt{3}}=\sqrt{25}=5\), which is rational. Check whether division forms a perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{\sqrt{75}}{\sqrt{3}}\). \(\frac{\sqrt{75}}{\sqrt{3}}=\sqrt{25}=5\), which is rational. Check whether division forms a perfect square.
Step 3
Exam Tip
\(\frac{\sqrt{75}}{\sqrt{3}}=\sqrt{25}=5\) है जो परिमेय है। भाग के बाद पूर्ण वर्ग बनने की जाँच करें।
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