संख्या रेखा पर \( \sqrt{48}-\sqrt{27} \) का सरल और सही मान कौन सा है?
What is the simplified correct value of \( \sqrt{48}-\sqrt{27} \) on the number line?
#number-line
#radical-difference
#simplification
A \( \sqrt{3} \)
B \(7\sqrt{3}\)
C \( \sqrt{21} \)
D \(3\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \( \sqrt{3} \)
Step 1
Concept
\( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \( \sqrt{3} \). Simplify the radicals first.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{3} \). \( \sqrt{48}=4\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \( \sqrt{3} \). Simplify the radicals first.
Step 3
Exam Tip
\( \sqrt{48}=4\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए अंतर \( \sqrt{3} \) है। पहले मूलों को सरल करें।
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यदि संख्या रेखा पर \(u=-\sqrt{2}-1\), तो (u) किस अंतराल में है?
If \(u=-\sqrt{2}-1\) on the number line, in which interval does (u) lie?
#number-line
#negative-expression
#interval
A ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
B ( -2 ) और ( -1 ) के बीच / Between ( -2 ) and ( -1 )
C ( -1 ) और (0) के बीच / Between ( -1 ) and (0)
D (2) और (3) के बीच / Between (2) and (3)
Explanation opens after your attempt
Correct Answer
A. ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
Step 1
Concept
\( -\sqrt{2}-1\approx-2.414 \), so it lies between (-3) and (-2). Estimate negative sums carefully.
Step 2
Why this answer is correct
The correct answer is A. ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 ). \( -\sqrt{2}-1\approx-2.414 \), so it lies between (-3) and (-2). Estimate negative sums carefully.
Step 3
Exam Tip
\( -\sqrt{2}-1\approx-2.414 \), इसलिए यह (-3) और (-2) के बीच है। ऋणात्मक योगों में अनुमान सावधानी से करें।
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कौन सा मान \( \frac{9}{4} \) से बड़ा और \( \sqrt{6} \) से छोटा है?
Which value is greater than \( \frac{9}{4} \) and less than \( \sqrt{6} \)?
#number-line
#between-values
#fraction-root
A (2.4)
B (2.2)
C (2.5)
D (3.0)
Explanation opens after your attempt
Step 1
Concept
\( \frac{9}{4}=2.25 \) and \( \sqrt{6}\approx2.449 \). Therefore (2.4) lies between them.
Step 2
Why this answer is correct
The correct answer is A. (2.4). \( \frac{9}{4}=2.25 \) and \( \sqrt{6}\approx2.449 \). Therefore (2.4) lies between them.
Step 3
Exam Tip
\( \frac{9}{4}=2.25 \) और \( \sqrt{6}\approx2.449 \) है। इसलिए (2.4) इनके बीच है।
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यदि \( \sqrt{x}=3.9 \), तो संख्या रेखा पर (x) किस बिंदु से जुड़ा है?
If \( \sqrt{x}=3.9 \), with which point is (x) associated on the number line?
#number-line
#square-root-equation
#decimal-square
A (15.21)
B (7.8)
C (12.21)
D (3.09)
Explanation opens after your attempt
Correct Answer
A. (15.21)
Step 1
Concept
\(x=3.9^2=15.21\). Square both sides to remove the square root.
Step 2
Why this answer is correct
The correct answer is A. (15.21). \(x=3.9^2=15.21\). Square both sides to remove the square root.
Step 3
Exam Tip
\(x=3.9^2=15.21\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें।
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संख्या रेखा पर \( \sqrt{13}+\sqrt{13} \) का सरल रूप कौन सा है?
What is the simplified form of \( \sqrt{13}+\sqrt{13} \) on the number line?
#number-line
#radical-addition
#common-mistake
A \(2\sqrt{13}\)
B \( \sqrt{26} \)
C (13)
D (26)
Explanation opens after your attempt
Correct Answer
A. \(2\sqrt{13}\)
Step 1
Concept
Adding like radicals gives \( \sqrt{13}+\sqrt{13}=2\sqrt{13} \). Do not add the numbers inside the radicals directly.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{13}\). Adding like radicals gives \( \sqrt{13}+\sqrt{13}=2\sqrt{13} \). Do not add the numbers inside the radicals directly.
Step 3
Exam Tip
समान मूलों को जोड़ने पर \( \sqrt{13}+\sqrt{13}=2\sqrt{13} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं।
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यदि संख्या रेखा पर (x) ऐसा है कि \( -\sqrt{50}<x<-7 \), तो कौन सा मान संभव है?
If (x) on the number line satisfies \( -\sqrt{50}<x<-7 \), which value is possible?
#number-line
#inequality
#negative-root
A ( -7.05 )
B ( -7.20 )
C ( -6.90 )
D ( -8.00 )
Explanation opens after your attempt
Correct Answer
A. ( -7.05 )
Step 1
Concept
\( -\sqrt{50}\approx-7.071 \), so (x) must lie between (-7.071) and (-7). (-7.05) is correct.
Step 2
Why this answer is correct
The correct answer is A. ( -7.05 ). \( -\sqrt{50}\approx-7.071 \), so (x) must lie between (-7.071) and (-7). (-7.05) is correct.
Step 3
Exam Tip
\( -\sqrt{50}\approx-7.071 \), इसलिए (x) को (-7.071) और (-7) के बीच होना चाहिए। (-7.05) सही है।
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संख्या रेखा पर \( \sqrt{90} \) किस पूर्णांक के सबसे निकट है?
On the number line, \( \sqrt{90} \) is closest to which integer?
#number-line
#nearest-integer
#square-root
A (9)
B (10)
C (8)
D (11)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{90}\approx9.49 \), which is closer to (10) than to (9). Check distance for the nearest integer.
Step 2
Why this answer is correct
The correct answer is B. (10). \( \sqrt{90}\approx9.49 \), which is closer to (10) than to (9). Check distance for the nearest integer.
Step 3
Exam Tip
\( \sqrt{90}\approx9.49 \) है जो (9) की तुलना में (10) के अधिक निकट है। निकटतम पूर्णांक के लिए दूरी जाँचें।
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यदि (A=-6.25), \(B=-\sqrt{39}\), और \(C=-\frac{25}{4}\), तो (A), (B), (C) में कौन से दो बिंदु समान हैं?
If (A=-6.25), \(B=-\sqrt{39}\), and \(C=-\frac{25}{4}\), which two points among (A), (B), and (C) are equal?
#number-line
#equivalent-points
#fractions
A (A) और (C) / (A) and (C)
B (A) और (B) / (A) and (B)
C (B) और (C) / (B) and (C)
D कोई दो समान नहीं / No two are equal
Explanation opens after your attempt
Correct Answer
A. (A) और (C) / (A) and (C)
Step 1
Concept
\( -\frac{25}{4}=-6.25 \), so (A=C). Convert the fraction to a decimal for comparison.
Step 2
Why this answer is correct
The correct answer is A. (A) और (C) / (A) and (C). \( -\frac{25}{4}=-6.25 \), so (A=C). Convert the fraction to a decimal for comparison.
Step 3
Exam Tip
\( -\frac{25}{4}=-6.25 \), इसलिए (A=C) है। भिन्न को दशमलव में बदलकर तुलना करें।
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संख्या रेखा पर \( \frac{1}{\sqrt{4}} \) किस बिंदु के बराबर है?
On the number line, \( \frac{1}{\sqrt{4}} \) equals which point?
#number-line
#reciprocal
#exact-value
A \( \frac{1}{2} \)
B (2)
C \( \frac{1}{4} \)
D (4)
Explanation opens after your attempt
Correct Answer
A. \( \frac{1}{2} \)
Step 1
Concept
\( \sqrt{4}=2 \), so \( \frac{1}{\sqrt{4}}=\frac{1}{2} \). Simplify the root in the denominator first.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{1}{2} \). \( \sqrt{4}=2 \), so \( \frac{1}{\sqrt{4}}=\frac{1}{2} \). Simplify the root in the denominator first.
Step 3
Exam Tip
\( \sqrt{4}=2 \), इसलिए \( \frac{1}{\sqrt{4}}=\frac{1}{2} \)। हर में मूल को पहले सरल करें।
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यदि (P) संख्या रेखा पर \( \sqrt{49}+\sqrt{16} \) पर है, तो (P) का निर्देशांक क्या है?
If (P) is at \( \sqrt{49}+\sqrt{16} \) on the number line, what is the coordinate of (P)?
#number-line
#exact-roots
#addition
A (11)
B (13)
C (9)
D (65)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{49}=7 \) and \( \sqrt{16}=4 \), so the sum is (11). Find each square root first.
Step 2
Why this answer is correct
The correct answer is A. (11). \( \sqrt{49}=7 \) and \( \sqrt{16}=4 \), so the sum is (11). Find each square root first.
Step 3
Exam Tip
\( \sqrt{49}=7 \) और \( \sqrt{16}=4 \), इसलिए योग (11) है। पहले अलग-अलग वर्गमूल निकालें।
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कौन सा मान ( -2 ) और \( -\sqrt{3} \) के बीच संख्या रेखा पर स्थित है?
Which value lies between (-2) and \( -\sqrt{3} \) on the number line?
#number-line
#negative-interval
#between-values
A ( -1.8 )
B ( -1.6 )
C ( -2.2 )
D ( -1.0 )
Explanation opens after your attempt
Correct Answer
A. ( -1.8 )
Step 1
Concept
\( -\sqrt{3}\approx-1.732 \), and (-1.8) lies between it and (-2). Check left-to-right order in negative intervals.
Step 2
Why this answer is correct
The correct answer is A. ( -1.8 ). \( -\sqrt{3}\approx-1.732 \), and (-1.8) lies between it and (-2). Check left-to-right order in negative intervals.
Step 3
Exam Tip
\( -\sqrt{3}\approx-1.732 \) है और (-1.8) इसके तथा (-2) के बीच है। ऋणात्मक अंतराल में बाएँ से दाएँ क्रम देखें।
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संख्या रेखा पर \( \sqrt{7}-\sqrt{5} \) का सबसे उचित अनुमान कौन सा है?
Which is the most suitable estimate of \( \sqrt{7}-\sqrt{5} \) on the number line?
#number-line
#root-difference
#estimation
A (0.41)
B (1.00)
C (0.05)
D (0.90)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{7}\approx2.646 \) and \( \sqrt{5}\approx2.236 \), so the difference is about (0.41). The difference of nearby roots is small.
Step 2
Why this answer is correct
The correct answer is A. (0.41). \( \sqrt{7}\approx2.646 \) and \( \sqrt{5}\approx2.236 \), so the difference is about (0.41). The difference of nearby roots is small.
Step 3
Exam Tip
\( \sqrt{7}\approx2.646 \) और \( \sqrt{5}\approx2.236 \), इसलिए अंतर लगभग (0.41) है। निकट मूलों का अंतर छोटा होता है।
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यदि संख्या रेखा पर \(x=\sqrt{a}\) और (5.2<x<5.3), तो (a) के लिए कौन सा मान सही है?
If \(x=\sqrt{a}\) and (5.2<x<5.3) on the number line, which value of (a) is correct?
#number-line
#square-root-range
#inequality
A (28)
B (26)
C (30)
D (25)
Explanation opens after your attempt
Step 1
Concept
\(5.2^2=27.04\) and \(5.3^2=28.09\), so (a) must lie between them. (28) is correct.
Step 2
Why this answer is correct
The correct answer is A. (28). \(5.2^2=27.04\) and \(5.3^2=28.09\), so (a) must lie between them. (28) is correct.
Step 3
Exam Tip
\(5.2^2=27.04\) और \(5.3^2=28.09\), इसलिए (a) इनके बीच होना चाहिए। (28) सही है।
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किस विकल्प में \( -\sqrt{2} \), ( -1.42 ), और \( -\frac{7}{5} \) का सही बढ़ता क्रम है?
Which option gives the correct increasing order of \( -\sqrt{2} \), ( -1.42 ), and \( -\frac{7}{5} \)?
#number-line
#ordering
#negative-values
A \( -1.42,-\sqrt{2},-\frac{7}{5} \)
B \( -\frac{7}{5},-\sqrt{2},-1.42 \)
C \( -\sqrt{2},-\frac{7}{5},-1.42 \)
D \( -1.42,-\frac{7}{5},-\sqrt{2} \)
Explanation opens after your attempt
Correct Answer
A. \( -1.42,-\sqrt{2},-\frac{7}{5} \)
Step 1
Concept
Since ( -1.42<-1.414<-1.4 ), the order is \( -1.42,-\sqrt{2},-\frac{7}{5} \). For negative decimals the smaller value comes first.
Step 2
Why this answer is correct
The correct answer is A. \( -1.42,-\sqrt{2},-\frac{7}{5} \). Since ( -1.42<-1.414<-1.4 ), the order is \( -1.42,-\sqrt{2},-\frac{7}{5} \). For negative decimals the smaller value comes first.
Step 3
Exam Tip
( -1.42<-1.414<-1.4 ) के कारण क्रम \( -1.42,-\sqrt{2},-\frac{7}{5} \) है। ऋणात्मक दशमलवों में छोटी संख्या पहले आती है।
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संख्या रेखा पर \( \sqrt{80} \) का सरल रूप कौन सा है जिससे उसका स्थान समझना आसान हो?
Which simplified form of \( \sqrt{80} \) makes its position on the number line easier to understand?
#number-line
#simplifying-roots
#location
A \(4\sqrt{5}\)
B \(8\sqrt{5}\)
C \(5\sqrt{4}\)
D \(2\sqrt{20}\)
Explanation opens after your attempt
Correct Answer
A. \(4\sqrt{5}\)
Step 1
Concept
\( \sqrt{80}=\sqrt{16\cdot5}=4\sqrt{5} \). Factor out the largest perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(4\sqrt{5}\). \( \sqrt{80}=\sqrt{16\cdot5}=4\sqrt{5} \). Factor out the largest perfect square.
Step 3
Exam Tip
\( \sqrt{80}=\sqrt{16\cdot5}=4\sqrt{5} \) है। सबसे बड़ा पूर्ण वर्ग बाहर निकालें।
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यदि \( \frac{a}{10} \) संख्या रेखा पर \( \sqrt{2} \) और (1.5) के बीच है, तो (a) का कौन सा पूर्णांक मान संभव है?
If \( \frac{a}{10} \) lies between \( \sqrt{2} \) and (1.5) on the number line, which integer value of (a) is possible?
#number-line
#parameter
#between-values
A (14.5)
B (13)
C (15)
D (16)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{2}\approx1.414 \), so \( \frac{a}{10} \) must be between (1.414) and (1.5). (a=14.5) gives (1.45).
Step 2
Why this answer is correct
The correct answer is A. (14.5). \( \sqrt{2}\approx1.414 \), so \( \frac{a}{10} \) must be between (1.414) and (1.5). (a=14.5) gives (1.45).
Step 3
Exam Tip
\( \sqrt{2}\approx1.414 \), इसलिए \( \frac{a}{10} \) को (1.414) और (1.5) के बीच होना चाहिए। (a=14.5) से (1.45) मिलता है।
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संख्या रेखा पर \(3-\sqrt{2}\) और \( \frac{8}{5} \) की तुलना में कौन सा कथन सही है?
Which statement is correct when comparing \(3-\sqrt{2}\) and \( \frac{8}{5} \) on the number line?
#number-line
#comparison
#root-expression
A \(3-\sqrt{2}<\frac{8}{5}\)
B \(3-\sqrt{2}>\frac{8}{5}\)
C \(3-\sqrt{2}=\frac{8}{5}\)
D दोनों (-1) से छोटे हैं / Both are less than (-1)
Explanation opens after your attempt
Correct Answer
A. \(3-\sqrt{2}<\frac{8}{5}\)
Step 1
Concept
\(3-\sqrt{2}\approx1.586\) and \( \frac{8}{5}=1.6 \). Therefore the first value is slightly smaller.
Step 2
Why this answer is correct
The correct answer is A. \(3-\sqrt{2}<\frac{8}{5}\). \(3-\sqrt{2}\approx1.586\) and \( \frac{8}{5}=1.6 \). Therefore the first value is slightly smaller.
Step 3
Exam Tip
\(3-\sqrt{2}\approx1.586\) और \( \frac{8}{5}=1.6 \) है। इसलिए पहला मान थोड़ा छोटा है।
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किस संख्या की (0) से दूरी संख्या रेखा पर \( \sqrt{17} \) है और वह (0) के बाईं ओर है?
Which number has distance \( \sqrt{17} \) from (0) and lies to the left of (0) on the number line?
#number-line
#distance-from-zero
#negative-root
A \( -\sqrt{17} \)
B \( \sqrt{17} \)
C (17)
D ( -17 )
Explanation opens after your attempt
Correct Answer
A. \( -\sqrt{17} \)
Step 1
Concept
The point on the left is negative and its distance is \( \sqrt{17} \). Therefore the number is \( -\sqrt{17} \).
Step 2
Why this answer is correct
The correct answer is A. \( -\sqrt{17} \). The point on the left is negative and its distance is \( \sqrt{17} \). Therefore the number is \( -\sqrt{17} \).
Step 3
Exam Tip
बाईं ओर का बिंदु ऋणात्मक होगा और दूरी \( \sqrt{17} \) है। इसलिए संख्या \( -\sqrt{17} \) है।
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यदि \(A=-\sqrt{28}\), (B=-5.3), और \(C=-\frac{16}{3}\), तो संख्या रेखा पर सबसे बाईं ओर कौन है?
If \(A=-\sqrt{28}\), (B=-5.3), and \(C=-\frac{16}{3}\), which is farthest left on the number line?
#number-line
#leftmost-point
#negative-comparison
A (C)
B (A)
C (B)
D तीनों समान हैं / All three are equal
Explanation opens after your attempt
Step 1
Concept
\(A\approx-5.292\), (B=-5.3), and \(C\approx-5.333\). The smallest number is (C).
Step 2
Why this answer is correct
The correct answer is A. (C). \(A\approx-5.292\), (B=-5.3), and \(C\approx-5.333\). The smallest number is (C).
Step 3
Exam Tip
\(A\approx-5.292\), (B=-5.3), और \(C\approx-5.333\) है। सबसे छोटी संख्या (C) है।
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कौन सा मान \( \sqrt{3}+\frac{1}{4} \) से छोटा और (2) से बड़ा है?
Which value is greater than \( \sqrt{3}+\frac{1}{4} \) and less than (2)?
#number-line
#between-values
#irrational-expression
A (1.99)
B (1.95)
C (1.90)
D (2.10)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{3}+\frac{1}{4}\approx1.982 \). Therefore (1.99) is greater than it and less than (2).
Step 2
Why this answer is correct
The correct answer is A. (1.99). \( \sqrt{3}+\frac{1}{4}\approx1.982 \). Therefore (1.99) is greater than it and less than (2).
Step 3
Exam Tip
\( \sqrt{3}+\frac{1}{4}\approx1.982 \) है। इसलिए (1.99) इससे बड़ा और (2) से छोटा है।
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संख्या रेखा पर \( \sqrt{\frac{49}{121}} \) किसके बराबर है?
On the number line, \( \sqrt{\frac{49}{121}} \) is equal to what?
#number-line
#fraction-root
#exact-value
A \( \frac{7}{11} \)
B \( \frac{49}{11} \)
C \( \frac{11}{7} \)
D \( \frac{7}{121} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{7}{11} \)
Step 1
Concept
\( \sqrt{\frac{49}{121}}=\frac{7}{11} \). Take the positive square root of numerator and denominator.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{7}{11} \). \( \sqrt{\frac{49}{121}}=\frac{7}{11} \). Take the positive square root of numerator and denominator.
Step 3
Exam Tip
\( \sqrt{\frac{49}{121}}=\frac{7}{11} \) है। अंश और हर दोनों का धनात्मक वर्गमूल लें।
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यदि (x) संख्या रेखा पर ( -2 ) और (1) के बीच है तथा (x) की ( -2 ) से दूरी \( \frac{5}{4} \) है, तो (x) क्या है?
If (x) lies between (-2) and (1) and its distance from (-2) is \( \frac{5}{4} \), what is (x)?
#number-line
#distance
#interval-condition
A \( -\frac{3}{4} \)
B \( -\frac{13}{4} \)
C \( \frac{5}{4} \)
D \( \frac{3}{4} \)
Explanation opens after your attempt
Correct Answer
A. \( -\frac{3}{4} \)
Step 1
Concept
Moving \( \frac{5}{4} \) to the right of (-2) gives \( -2+\frac{5}{4}=-\frac{3}{4} \). Use the given interval to choose the direction.
Step 2
Why this answer is correct
The correct answer is A. \( -\frac{3}{4} \). Moving \( \frac{5}{4} \) to the right of (-2) gives \( -2+\frac{5}{4}=-\frac{3}{4} \). Use the given interval to choose the direction.
Step 3
Exam Tip
(-2) से दाईं ओर \( \frac{5}{4} \) जाने पर \( -2+\frac{5}{4}=-\frac{3}{4} \) मिलता है। दिए गए अंतराल से सही दिशा चुनें।
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संख्या रेखा पर \( \frac{\sqrt{64}-3}{5} \) किस बिंदु के बराबर है?
On the number line, \( \frac{\sqrt{64}-3}{5} \) is equal to which point?
#number-line
#exact-expression
#operations
A (1)
B \( \frac{11}{5} \)
C \( \frac{5}{8} \)
D \( \frac{3}{5} \)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{64}=8 \), so \( \frac{8-3}{5}=1 \). Keep the order of operations correct.
Step 2
Why this answer is correct
The correct answer is A. (1). \( \sqrt{64}=8 \), so \( \frac{8-3}{5}=1 \). Keep the order of operations correct.
Step 3
Exam Tip
\( \sqrt{64}=8 \), इसलिए \( \frac{8-3}{5}=1 \)। संचालन का क्रम सही रखें।
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किस विकल्प में \( \sqrt{24} \) की संख्या रेखा पर सही दशमलव सीमा दी गई है?
Which option gives the correct decimal bound for \( \sqrt{24} \) on the number line?
#number-line
#decimal-bounds
#square-root
A \(4.8<\sqrt{24}<4.9\)
B \(4.6<\sqrt{24}<4.7\)
C \(5.0<\sqrt{24}<5.1\)
D \(3.8<\sqrt{24}<3.9\)
Explanation opens after your attempt
Correct Answer
A. \(4.8<\sqrt{24}<4.9\)
Step 1
Concept
\(4.8^2=23.04\) and \(4.9^2=24.01\). Hence \( \sqrt{24} \) lies between them.
Step 2
Why this answer is correct
The correct answer is A. \(4.8<\sqrt{24}<4.9\). \(4.8^2=23.04\) and \(4.9^2=24.01\). Hence \( \sqrt{24} \) lies between them.
Step 3
Exam Tip
\(4.8^2=23.04\) और \(4.9^2=24.01\) है। इसलिए \( \sqrt{24} \) इनके बीच है।
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यदि \(a=\sqrt{8}\), \(b=\frac{14}{5}\), और (c=2.81), तो संख्या रेखा पर सबसे बड़ा कौन है?
If \(a=\sqrt{8}\), \(b=\frac{14}{5}\), and (c=2.81), which is greatest on the number line?
#number-line
#greatest-value
#comparison
A (a)
B (b)
C (c)
D तीनों समान हैं / All three are equal
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{8}\approx2.828 \), \( \frac{14}{5}=2.8 \), and (c=2.81). Therefore (a) is the greatest.
Step 2
Why this answer is correct
The correct answer is A. (a). \( \sqrt{8}\approx2.828 \), \( \frac{14}{5}=2.8 \), and (c=2.81). Therefore (a) is the greatest.
Step 3
Exam Tip
\( \sqrt{8}\approx2.828 \), \( \frac{14}{5}=2.8 \), और (2.81) है। इसलिए (a) सबसे बड़ा है।
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संख्या रेखा पर \( \sqrt{63} \) के सबसे निकट कौन सा दशमलव मान है?
Which decimal value is closest to \( \sqrt{63} \) on the number line?
#number-line
#estimation
#square-root
A (7.94)
B (7.50)
C (8.20)
D (6.90)
Explanation opens after your attempt
Step 1
Concept
\( \sqrt{63}\approx7.94 \) because \(7.94^2\) is close to (63). Check nearby squares for large roots.
Step 2
Why this answer is correct
The correct answer is A. (7.94). \( \sqrt{63}\approx7.94 \) because \(7.94^2\) is close to (63). Check nearby squares for large roots.
Step 3
Exam Tip
\( \sqrt{63}\approx7.94 \) क्योंकि \(7.94^2\) लगभग (63) है। बड़े मूलों में निकट वर्ग जाँचें।
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कौन सा बिंदु \( \frac{7}{10} \) से \( \frac{3}{20} \) इकाई बाईं ओर है?
Which point is \( \frac{3}{20} \) unit to the left of \( \frac{7}{10} \)?
#number-line
#fraction-distance
#direction
A \( \frac{11}{20} \)
B \( \frac{17}{20} \)
C \( \frac{1}{2} \)
D \( \frac{3}{10} \)
Explanation opens after your attempt
Correct Answer
A. \( \frac{11}{20} \)
Step 1
Concept
Moving left gives \( \frac{7}{10}-\frac{3}{20}=\frac{11}{20} \). Subtract according to direction.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{11}{20} \). Moving left gives \( \frac{7}{10}-\frac{3}{20}=\frac{11}{20} \). Subtract according to direction.
Step 3
Exam Tip
बाईं ओर जाने पर \( \frac{7}{10}-\frac{3}{20}=\frac{11}{20} \) मिलता है। दिशा के अनुसार घटाएँ।
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यदि \(p=-\sqrt{45}+2\), तो (p) संख्या रेखा पर किस अंतराल में होगा?
If \(p=-\sqrt{45}+2\), in which interval will (p) lie on the number line?
#number-line
#negative-expression
#estimation
A ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
B ( -4 ) और ( -3 ) के बीच / Between ( -4 ) and ( -3 )
C ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 )
D (4) और (5) के बीच / Between (4) and (5)
Explanation opens after your attempt
Correct Answer
A. ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 )
Step 1
Concept
\( \sqrt{45}\approx6.708 \), so \(p\approx-4.708\). Hence it lies between (-5) and (-4).
Step 2
Why this answer is correct
The correct answer is A. ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 ). \( \sqrt{45}\approx6.708 \), so \(p\approx-4.708\). Hence it lies between (-5) and (-4).
Step 3
Exam Tip
\( \sqrt{45}\approx6.708 \), इसलिए \(p\approx-4.708\) है। इसलिए यह (-5) और (-4) के बीच है।
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संख्या रेखा पर \( \sqrt{37}+1 \) किस दो लगातार पूर्णांकों के बीच है?
Between which two consecutive integers is \( \sqrt{37}+1 \) on the number line?
#number-line
#root-expression
#integer-bounds
A (7) और (8) / (7) and (8)
B (6) और (7) / (6) and (7)
C (8) और (9) / (8) and (9)
D (5) और (6) / (5) and (6)
Explanation opens after your attempt
Correct Answer
A. (7) और (8) / (7) and (8)
Step 1
Concept
Since \(6<\sqrt{37}<7\), \(7<\sqrt{37}+1<8\). First find the bounds of the square root.
Step 2
Why this answer is correct
The correct answer is A. (7) और (8) / (7) and (8). Since \(6<\sqrt{37}<7\), \(7<\sqrt{37}+1<8\). First find the bounds of the square root.
Step 3
Exam Tip
\(6<\sqrt{37}<7\) इसलिए \(7<\sqrt{37}+1<8\)। पहले वर्गमूल की सीमा निकालें।
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कौन सा विकल्प संख्या रेखा पर \( \sqrt{0.0081} \) का सही मान देता है?
Which option gives the correct value of \( \sqrt{0.0081} \) on the number line?
#number-line
#small-decimal-root
#place-value
A (0.09)
B (0.9)
C (0.009)
D (0.81)
Explanation opens after your attempt
Step 1
Concept
\(0.09^2=0.0081\), so the square root is (0.09). Count decimal places carefully.
Step 2
Why this answer is correct
The correct answer is A. (0.09). \(0.09^2=0.0081\), so the square root is (0.09). Count decimal places carefully.
Step 3
Exam Tip
\(0.09^2=0.0081\) इसलिए वर्गमूल (0.09) है। दशमलव स्थानों को ध्यान से गिनें।
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