संख्या रेखा पर \(\sqrt{45}\) किस पूर्णांक के सबसे निकट होगा?
On the number line, \(\sqrt{45}\) will be closest to which integer?
#number-line
#estimation
#square-root
#nearest-integer
A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{45}\) is about (6.7), so it is closer to (7). Nearby perfect squares (36) and (49) help in estimation.
Step 2
Why this answer is correct
The correct answer is C. (7). \(\sqrt{45}\) is about (6.7), so it is closer to (7). Nearby perfect squares (36) and (49) help in estimation.
Step 3
Exam Tip
\(\sqrt{45}\) लगभग (6.7) है इसलिए यह (7) के अधिक पास है। अनुमान में पास के पूर्ण वर्ग (36) और (49) उपयोगी हैं।
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संख्या रेखा पर \(-\sqrt{16}\) और (2.5) के बीच की दूरी कितनी है?
What is the distance between \(-\sqrt{16}\) and (2.5) on the number line?
#number-line
#distance
#square-root
#absolute-value
A (4.5)
B (5.5)
C (6.5)
D (8.5)
Explanation opens after your attempt
Step 1
Concept
\(-\sqrt{16}=-4\), so the distance is (|2.5-(-4)|=6.5). Distance is always taken positive.
Step 2
Why this answer is correct
The correct answer is C. (6.5). \(-\sqrt{16}=-4\), so the distance is (|2.5-(-4)|=6.5). Distance is always taken positive.
Step 3
Exam Tip
\(-\sqrt{16}=-4\), इसलिए दूरी (|2.5-(-4)|=6.5) है। दूरी हमेशा धनात्मक लेते हैं।
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संख्या रेखा पर \(\sqrt{26}\) किस दो क्रमागत पूर्णांकों के बीच होगा?
Between which two consecutive integers will \(\sqrt{26}\) lie on the number line?
#number-line
#irrational-numbers
#square-root
#comparison
A (4) और (5) / (4) and (5)
B (5) और (6) / (5) and (6)
C (6) और (7) / (6) and (7)
D (7) और (8) / (7) and (8)
Explanation opens after your attempt
Correct Answer
B. (5) और (6) / (5) and (6)
Step 1
Concept
Since \(5^2<26<6^2\), \(\sqrt{26}\) lies between (5) and (6). Check nearby perfect squares.
Step 2
Why this answer is correct
The correct answer is B. (5) और (6) / (5) and (6). Since \(5^2<26<6^2\), \(\sqrt{26}\) lies between (5) and (6). Check nearby perfect squares.
Step 3
Exam Tip
क्योंकि \(5^2<26<6^2\), इसलिए \(\sqrt{26}\) (5) और (6) के बीच होगा। पास के पूर्ण वर्ग देखें।
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संख्या रेखा पर \(\sqrt{17}\) बनाने के लिए समकोण त्रिभुज की लंब भुजाएं (4) और (1) ली गई हैं। कर्ण की लंबाई क्या होगी?
To construct \(\sqrt{17}\) on the number line, the perpendicular sides of a right triangle are taken as (4) and (1). What will be the length of the hypotenuse?
#number-line
#square-root
#construction
#pythagoras
A \(\sqrt{15}\)
B \(\sqrt{17}\)
C (5)
D (17)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{17}\)
Step 1
Concept
The hypotenuse is \(\sqrt{4^2+1^2}=\sqrt{17}\). Use Pythagoras in this type of construction.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{17}\). The hypotenuse is \(\sqrt{4^2+1^2}=\sqrt{17}\). Use Pythagoras in this type of construction.
Step 3
Exam Tip
कर्ण \(=\sqrt{4^2+1^2}=\sqrt{17}\) होगा। ऐसी रचना में पाइथागोरस प्रमेय लगाएं।
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संख्या रेखा पर \(\sqrt{10}\) को किस दो पूर्णांकों के बीच सही रूप से दर्शाया जाएगा?
Between which two integers will \(\sqrt{10}\) be correctly represented on the number line?
#polynomials
#number-line
#square-root
#medium
A (2) और (3) / (2) and (3)
B (3) और (4) / (3) and (4)
C (4) और (5) / (4) and (5)
D (10) और (11) / (10) and (11)
Explanation opens after your attempt
Correct Answer
B. (3) और (4) / (3) and (4)
Step 1
Concept
Since \(3^2=9\) and \(4^2=16\), \(\sqrt{10}\) lies between (3) and (4). In exams, bracket square roots between perfect squares.
Step 2
Why this answer is correct
The correct answer is B. (3) और (4) / (3) and (4). Since \(3^2=9\) and \(4^2=16\), \(\sqrt{10}\) lies between (3) and (4). In exams, bracket square roots between perfect squares.
Step 3
Exam Tip
क्योंकि \(3^2=9\) और \(4^2=16\), इसलिए \(\sqrt{10}\) (3) और (4) के बीच है। परीक्षा में वर्गमूल को पूर्ण वर्गों से घेरें।
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संख्या रेखा पर \(\sqrt{8}\) और (3) के बीच संबंध कौन सा सही है?
Which relation between \(\sqrt{8}\) and (3) on the number line is correct?
#number-line
#square-root
#inequality
#comparison
A \(\sqrt{8}>3\)
B \(\sqrt{8}=3\)
C \(\sqrt{8}<3\)
D \(\sqrt{8}=8\)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{8}<3\)
Step 1
Concept
Since (8<9), \(\sqrt{8}<3\). For comparison, think in terms of squares.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{8}<3\). Since (8<9), \(\sqrt{8}<3\). For comparison, think in terms of squares.
Step 3
Exam Tip
क्योंकि (8<9), इसलिए \(\sqrt{8}<3\) है। तुलना के लिए दोनों ओर वर्ग सोचें।
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एक छात्र ने कहा कि \(\sqrt{12}\) संख्या रेखा पर (12) के पास होगा। सही सुधार क्या है?
A student said that \(\sqrt{12}\) will be near (12) on the number line. What is the correct correction?
#number-line
#common-mistake
#square-root
#conceptual
A यह (1) और (2) के बीच होगा / It will be between (1) and (2)
B यह (2) और (3) के बीच होगा / It will be between (2) and (3)
C यह (3) और (4) के बीच होगा / It will be between (3) and (4)
D यह (12) पर ही होगा / It will be exactly at (12)
Explanation opens after your attempt
Correct Answer
C. यह (3) और (4) के बीच होगा / It will be between (3) and (4)
Step 1
Concept
Since \(3^2<12<4^2\), \(\sqrt{12}\) lies between (3) and (4). A square root can be much smaller than the number.
Step 2
Why this answer is correct
The correct answer is C. यह (3) और (4) के बीच होगा / It will be between (3) and (4). Since \(3^2<12<4^2\), \(\sqrt{12}\) lies between (3) and (4). A square root can be much smaller than the number.
Step 3
Exam Tip
क्योंकि \(3^2<12<4^2\), इसलिए \(\sqrt{12}\) (3) और (4) के बीच है। वर्गमूल संख्या को छोटा कर सकता है।
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संख्या रेखा पर \(\sqrt{a^2}\) के लिए यदि (a=-4) हो तो बिंदु कौन सा होगा?
For \(\sqrt{a^2}\) on the number line, if (a=-4), which point will it be?
#number-line
#absolute-value
#square-root
#common-mistake
A (-4)
B (4)
C (16)
D (-16)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{a^2}=|a|\), so for (a=-4) the value is (4). The principal square root is not negative.
Step 2
Why this answer is correct
The correct answer is B. (4). \(\sqrt{a^2}=|a|\), so for (a=-4) the value is (4). The principal square root is not negative.
Step 3
Exam Tip
\(\sqrt{a^2}=|a|\), इसलिए (a=-4) पर मान (4) होगा। वर्गमूल का मुख्य मान ऋणात्मक नहीं होता।
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कौन सा कथन सत्य है: संख्या रेखा पर \(\sqrt{2}\) और \(\sqrt{3}\) में कौन दाईं ओर है?
Which statement is true: on the number line, which is to the right, \(\sqrt{2}\) or \(\sqrt{3}\)?
#number-line
#square-root
#order
#comparison
A \(\sqrt{2}\) दाईं ओर है / \(\sqrt{2}\) is to the right
B \(\sqrt{3}\) दाईं ओर है / \(\sqrt{3}\) is to the right
C दोनों एक ही बिंदु हैं / Both are the same point
D दोनों (0) से बाईं ओर हैं / Both are left of (0)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{3}\) दाईं ओर है / \(\sqrt{3}\) is to the right
Step 1
Concept
Since (3>2), \(\sqrt{3}>\sqrt{2}\). For positive square roots, the root of the larger number is larger.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{3}\) दाईं ओर है / \(\sqrt{3}\) is to the right. Since (3>2), \(\sqrt{3}>\sqrt{2}\). For positive square roots, the root of the larger number is larger.
Step 3
Exam Tip
क्योंकि (3>2), इसलिए \(\sqrt{3}>\sqrt{2}\) है। धनात्मक वर्गमूलों में बड़ी संख्या का वर्गमूल बड़ा होता है।
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संख्या रेखा पर \(\sqrt{20}\) किस पूर्णांक के सबसे निकट है?
On the number line, \(\sqrt{20}\) is closest to which integer?
#number-line
#nearest-integer
#square-root
#estimation
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{20}\) is about (4.47), so it is closer to (4). Place \(\sqrt{20}\) between (4) and (5) and compare distances.
Step 2
Why this answer is correct
The correct answer is B. (4). \(\sqrt{20}\) is about (4.47), so it is closer to (4). Place \(\sqrt{20}\) between (4) and (5) and compare distances.
Step 3
Exam Tip
\(\sqrt{20}\) लगभग (4.47) है इसलिए यह (4) के अधिक पास है। \(\sqrt{20}\) को (4) और (5) के बीच रखकर दूरी सोचें।
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संख्या रेखा पर \(\sqrt{3}\) का सबसे सही अनुमान कौन सा है?
Which is the most accurate estimate of \(\sqrt{3}\) on the number line?
#number-line
#square-root
#estimation
#irrational-numbers
A (1.1)
B (1.7)
C (2.3)
D (3.1)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{3}\) is about (1.732), so (1.7) is closest. For estimation place \(\sqrt{3}\) between (1) and (2).
Step 2
Why this answer is correct
The correct answer is B. (1.7). \(\sqrt{3}\) is about (1.732), so (1.7) is closest. For estimation place \(\sqrt{3}\) between (1) and (2).
Step 3
Exam Tip
\(\sqrt{3}\) लगभग (1.732) है इसलिए (1.7) सबसे पास है। अनुमान के लिए \(\sqrt{3}\) को (1) और (2) के बीच रखें।
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यदि \(\sqrt{a}\) संख्या रेखा पर (5) से थोड़ा अधिक और (6) से कम है तो (a) किस सीमा में होगा?
If \(\sqrt{a}\) is slightly greater than (5) and less than (6) on the number line, in which range will (a) lie?
#number-line
#inequality
#square-root
#range
A (5<a<6)
B (10<a<12)
C (25<a<36)
D (36<a<49)
Explanation opens after your attempt
Correct Answer
C. (25<a<36)
Step 1
Concept
If \(5<\sqrt{a}<6\), then (25<a<36). Square the root bounds to get the range of (a).
Step 2
Why this answer is correct
The correct answer is C. (25<a<36). If \(5<\sqrt{a}<6\), then (25<a<36). Square the root bounds to get the range of (a).
Step 3
Exam Tip
\(5<\sqrt{a}<6\) होने पर (25<a<36) होगा। वर्गमूल की सीमा को वर्ग करके (a) की सीमा मिलती है।
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संख्या रेखा पर \(\sqrt{18}\) के सबसे निकट कौन सा पूर्णांक है?
Which integer is closest to \(\sqrt{18}\) on the number line?
#number-line
#estimation
#square-root
#nearest-integer
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{18}\) is about (4.24), so it is closer to (4). For estimation, check nearby perfect squares (16) and (25).
Step 2
Why this answer is correct
The correct answer is B. (4). \(\sqrt{18}\) is about (4.24), so it is closer to (4). For estimation, check nearby perfect squares (16) and (25).
Step 3
Exam Tip
\(\sqrt{18}\) लगभग (4.24) है इसलिए यह (4) के अधिक पास है। अनुमान के लिए पास के पूर्ण वर्ग (16) और (25) देखें।
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यदि \(\sqrt{n}\) संख्या रेखा पर (4) और (5) के बीच है तो (n) के लिए कौन सा मान संभव है?
If \(\sqrt{n}\) lies between (4) and (5) on the number line, which value of (n) is possible?
#number-line
#square-root
#inequality
#reasoning
A (12)
B (18)
C (21)
D (30)
Explanation opens after your attempt
Step 1
Concept
For \(\sqrt{n}\) to lie between (4) and (5), (16<n<25) is needed. Among the options (21) is correct.
Step 2
Why this answer is correct
The correct answer is C. (21). For \(\sqrt{n}\) to lie between (4) and (5), (16<n<25) is needed. Among the options (21) is correct.
Step 3
Exam Tip
\(\sqrt{n}\) के (4) और (5) के बीच होने के लिए (16<n<25) चाहिए। दिए गए विकल्पों में (21) सही है।
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संख्या रेखा पर \(\sqrt{7}\) की स्थिति के बारे में कौन सा कथन सही है?
Which statement about the position of \(\sqrt{7}\) on the number line is correct?
#number-line
#irrational-numbers
#square-root
#common-mistake
A यह (2) से कम है / It is less than (2)
B यह (2) और (3) के बीच है / It is between (2) and (3)
C यह (3) और (4) के बीच है / It is between (3) and (4)
D यह (7) पर है / It is at (7)
Explanation opens after your attempt
Correct Answer
B. यह (2) और (3) के बीच है / It is between (2) and (3)
Step 1
Concept
Since \(2^2<7<3^2\), \(\sqrt{7}\) lies between (2) and (3). Taking \(\sqrt{7}\) as (7) is a common mistake.
Step 2
Why this answer is correct
The correct answer is B. यह (2) और (3) के बीच है / It is between (2) and (3). Since \(2^2<7<3^2\), \(\sqrt{7}\) lies between (2) and (3). Taking \(\sqrt{7}\) as (7) is a common mistake.
Step 3
Exam Tip
क्योंकि \(2^2<7<3^2\), इसलिए \(\sqrt{7}\), (2) और (3) के बीच होगा। \(\sqrt{7}\) को (7) समझना सामान्य गलती है।
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संख्या रेखा पर \(\sqrt{13}\) को बनाने के लिए (3) और (2) लंब भुजाओं वाला समकोण त्रिभुज बनाया जाए तो कर्ण क्या होगा?
To construct \(\sqrt{13}\) on the number line, if a right triangle has perpendicular sides (3) and (2), what is the hypotenuse?
#number-line
#construction
#pythagoras
#square-root
A \(\sqrt{5}\)
B \(\sqrt{11}\)
C \(\sqrt{13}\)
D (5)
Explanation opens after your attempt
Correct Answer
C. \(\sqrt{13}\)
Step 1
Concept
The hypotenuse is \(\sqrt{3^2+2^2}=\sqrt{13}\). Apply Pythagoras in a right triangle.
Step 2
Why this answer is correct
The correct answer is C. \(\sqrt{13}\). The hypotenuse is \(\sqrt{3^2+2^2}=\sqrt{13}\). Apply Pythagoras in a right triangle.
Step 3
Exam Tip
कर्ण \(=\sqrt{3^2+2^2}=\sqrt{13}\) होता है। समकोण त्रिभुज में पाइथागोरस प्रमेय लागू करें।
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संख्या रेखा पर \(\sqrt{10}\) किस दो क्रमागत पूर्णांकों के बीच स्थित होगा?
Between which two consecutive integers will \(\sqrt{10}\) be located on the number line?
#number-line
#square-root
#irrational-numbers
#comparison
A (2) और (3) / (2) and (3)
B (3) और (4) / (3) and (4)
C (4) और (5) / (4) and (5)
D (5) और (6) / (5) and (6)
Explanation opens after your attempt
Correct Answer
B. (3) और (4) / (3) and (4)
Step 1
Concept
Since \(3^2<10<4^2\), \(\sqrt{10}\) lies between (3) and (4). Use nearby perfect squares to locate roots.
Step 2
Why this answer is correct
The correct answer is B. (3) और (4) / (3) and (4). Since \(3^2<10<4^2\), \(\sqrt{10}\) lies between (3) and (4). Use nearby perfect squares to locate roots.
Step 3
Exam Tip
क्योंकि \(3^2<10<4^2\), इसलिए \(\sqrt{10}\), (3) और (4) के बीच होगा। वर्गमूल की स्थिति के लिए पास के पूर्ण वर्ग देखें।
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संख्या रेखा पर \(\sqrt{5}\) को सही स्थान पर रखने के लिए किस तथ्य का उपयोग किया जा सकता है?
Which fact can be used to place \(\sqrt{5}\) correctly on the number line?
#number-line
#irrational-numbers
#square-root
#comparison
A \(2^2<5<3^2\)
B \(5^2<2<6^2\)
C \(1^2<5<2^2\)
D \(3^2<5<4^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^2<5<3^2\)
Step 1
Concept
Since (4<5<9), \(\sqrt{5}\) lies between (2) and (3). Comparing squares helps locate square roots.
Step 2
Why this answer is correct
The correct answer is A. \(2^2<5<3^2\). Since (4<5<9), \(\sqrt{5}\) lies between (2) and (3). Comparing squares helps locate square roots.
Step 3
Exam Tip
क्योंकि (4<5<9), इसलिए \(\sqrt{5}\), (2) और (3) के बीच होगा। वर्गों की तुलना से वर्गमूल की स्थिति मिलती है।
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संख्या रेखा पर \(\sqrt{2}\) को बनाने के लिए समकोण त्रिभुज की दो लंब भुजाएं (1) और (1) ली गई हैं। कर्ण की लंबाई क्या होगी?
To construct \(\sqrt{2}\) on the number line, two perpendicular sides of a right triangle are taken as (1) and (1). What will be the length of the hypotenuse?
#number-line
#real-numbers
#square-root
#construction
A (1)
B \(\sqrt{2}\)
C (2)
D \(\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
B. \(\sqrt{2}\)
Step 1
Concept
By Pythagoras the hypotenuse is \(\sqrt{1^2+1^2}=\sqrt{2}\). In such constructions always add the squares of perpendicular sides.
Step 2
Why this answer is correct
The correct answer is B. \(\sqrt{2}\). By Pythagoras the hypotenuse is \(\sqrt{1^2+1^2}=\sqrt{2}\). In such constructions always add the squares of perpendicular sides.
Step 3
Exam Tip
पाइथागोरस से कर्ण \(=\sqrt{1^2+1^2}=\sqrt{2}\) होगा। ऐसी रचनाओं में वर्गों का योग जरूर देखें।
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संख्या रेखा पर \(\sqrt{5}\) किस दो क्रमागत पूर्णांकों के बीच होगा?
Between which two consecutive integers will \(\sqrt{5}\) lie on the number line?
#number-line
#irrational-numbers
#square-root
#easy
A (1) और (2) / (1) and (2)
B (2) और (3) / (2) and (3)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
B. (2) और (3) / (2) and (3)
Step 1
Concept
Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Use squares to locate square roots quickly.
Step 2
Why this answer is correct
The correct answer is B. (2) और (3) / (2) and (3). Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Use squares to locate square roots quickly.
Step 3
Exam Tip
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\), (2) और (3) के बीच होगा। वर्गों से वर्गमूल की स्थिति जल्दी मिलती है।
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संख्या रेखा पर \(\sqrt{9}\) किस बिंदु के समान है?
On the number line \(\sqrt{9}\) is the same as which point?
#number-line
#square-root
#perfect-square
#easy
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.
Step 2
Why this answer is correct
The correct answer is B. (3). \(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.
Step 3
Exam Tip
\(\sqrt{9}=3\), इसलिए यह बिंदु (3) पर होगा। पूर्ण वर्गों के वर्गमूल तुरंत पहचानें।
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संख्या रेखा पर \(\sqrt{13}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{13}\) lie on the number line?
#square-root
#comparison
#number-line
A (3) और (4) / (3) and (4)
B (2) और (3) / (2) and (3)
C (4) और (5) / (4) and (5)
D (1) और (2) / (1) and (2)
Explanation opens after your attempt
Correct Answer
A. (3) और (4) / (3) and (4)
Step 1
Concept
Since \(3^2<13<4^2\), \(\sqrt{13}\) lies between (3) and (4). Comparing squares makes it easy.
Step 2
Why this answer is correct
The correct answer is A. (3) और (4) / (3) and (4). Since \(3^2<13<4^2\), \(\sqrt{13}\) lies between (3) and (4). Comparing squares makes it easy.
Step 3
Exam Tip
क्योंकि \(3^2<13<4^2\), इसलिए \(\sqrt{13}\), (3) और (4) के बीच है। वर्गों से तुलना आसान होती है।
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संख्या रेखा पर \(\sqrt{8}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{8}\) lie on the number line?
#square-root
#number-line
#comparison
A (2) और (3) / (2) and (3)
B (1) और (2) / (1) and (2)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
A. (2) और (3) / (2) and (3)
Step 1
Concept
Since \(2^2<8<3^2\), \(\sqrt{8}\) lies between (2) and (3). First identify nearby perfect squares.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). Since \(2^2<8<3^2\), \(\sqrt{8}\) lies between (2) and (3). First identify nearby perfect squares.
Step 3
Exam Tip
क्योंकि \(2^2<8<3^2\), इसलिए \(\sqrt{8}\), (2) और (3) के बीच है। पहले पास के पूर्ण वर्ग पहचानें।
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संख्या रेखा पर \(\sqrt{10}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{10}\) lie on the number line?
#square-root
#comparison
#number-line
A (3) और (4) / (3) and (4)
B (2) और (3) / (2) and (3)
C (4) और (5) / (4) and (5)
D (1) और (2) / (1) and (2)
Explanation opens after your attempt
Correct Answer
A. (3) और (4) / (3) and (4)
Step 1
Concept
Since \(3^2<10<4^2\), \(\sqrt{10}\) lies between (3) and (4). Always place (n) between nearby perfect squares.
Step 2
Why this answer is correct
The correct answer is A. (3) और (4) / (3) and (4). Since \(3^2<10<4^2\), \(\sqrt{10}\) lies between (3) and (4). Always place (n) between nearby perfect squares.
Step 3
Exam Tip
क्योंकि \(3^2<10<4^2\), इसलिए \(\sqrt{10}\), (3) और (4) के बीच है। हमेशा (n) को पास के पूर्ण वर्गों के बीच रखें।
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संख्या रेखा पर \(\sqrt{16}\) का स्थान कौन-सा है?
What is the position of \(\sqrt{16}\) on the number line?
#perfect-square
#number-line
#square-root
A (4)
B (8)
C (16)
D -(4)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{16}=4\), so its position is (4). Square roots of perfect squares can be identified directly.
Step 2
Why this answer is correct
The correct answer is A. (4). \(\sqrt{16}=4\), so its position is (4). Square roots of perfect squares can be identified directly.
Step 3
Exam Tip
\(\sqrt{16}=4\), इसलिए इसका स्थान (4) है। पूर्ण वर्गों के वर्गमूल सीधे पहचाने जा सकते हैं।
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संख्या रेखा पर \(\sqrt{9}\) किस संख्या के बराबर है?
Which number is equal to \(\sqrt{9}\) on the number line?
#perfect-square
#square-root
#number-line
A (3)
B (9)
C \(\frac{1}{3}\)
D -(3)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
Step 2
Why this answer is correct
The correct answer is A. (3). \(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
Step 3
Exam Tip
\(\sqrt{9}=3\), इसलिए यह (3) के बिंदु पर होगा। वर्गमूल का मुख्य मान धनात्मक लिया जाता है।
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संख्या रेखा पर \(\sqrt{5}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{5}\) lie on the number line?
#square-root
#number-line
#irrational-number
A (2) और (3) / (2) and (3)
B (1) और (2) / (1) and (2)
C (3) और (4) / (3) and (4)
D (4) और (5) / (4) and (5)
Explanation opens after your attempt
Correct Answer
A. (2) और (3) / (2) and (3)
Step 1
Concept
Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Perfect squares quickly give the interval.
Step 2
Why this answer is correct
The correct answer is A. (2) और (3) / (2) and (3). Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Perfect squares quickly give the interval.
Step 3
Exam Tip
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\), (2) और (3) के बीच है। पूर्ण वर्गों से अंतराल जल्दी मिल जाता है।
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संख्या रेखा पर \(\sqrt{3}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{3}\) lie on the number line?
#square-root
#number-line
#comparison
A (1) और (2) / (1) and (2)
B (2) और (3) / (2) and (3)
C (3) और (4) / (3) and (4)
D (0) और (1) / (0) and (1)
Explanation opens after your attempt
Correct Answer
A. (1) और (2) / (1) and (2)
Step 1
Concept
Since \(1^2<3<2^2\), \(\sqrt{3}\) lies between (1) and (2). For square roots, check nearby perfect squares.
Step 2
Why this answer is correct
The correct answer is A. (1) और (2) / (1) and (2). Since \(1^2<3<2^2\), \(\sqrt{3}\) lies between (1) and (2). For square roots, check nearby perfect squares.
Step 3
Exam Tip
क्योंकि \(1^2<3<2^2\), इसलिए \(\sqrt{3}\), (1) और (2) के बीच है। वर्गमूल के लिए नजदीकी पूर्ण वर्ग देखें।
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संख्या रेखा पर \(\sqrt{2}\) किस दो पूर्णांकों के बीच स्थित है?
Between which two integers does \(\sqrt{2}\) lie on the number line?
#square-root
#number-line
#irrational-number
A (1) और (2) / (1) and (2)
B (0) और (1) / (0) and (1)
C (2) और (3) / (2) and (3)
D (3) और (4) / (3) and (4)
Explanation opens after your attempt
Correct Answer
A. (1) और (2) / (1) and (2)
Step 1
Concept
Since \(1^2<2<2^2\), we get \(1<\sqrt{2}<2\). Compare squares to locate a square root.
Step 2
Why this answer is correct
The correct answer is A. (1) और (2) / (1) and (2). Since \(1^2<2<2^2\), we get \(1<\sqrt{2}<2\). Compare squares to locate a square root.
Step 3
Exam Tip
क्योंकि \(1^2<2<2^2\), इसलिए \(1<\sqrt{2}<2\)। वर्गों की तुलना करके वर्गमूल का स्थान पहचानें।
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यदि \(A=19+6\sqrt{10}\), तो \(\sqrt{A}\) का सरल रूप क्या है?
If \(A=19+6\sqrt{10}\), what is the simplified form of \(\sqrt{A}\)?
#surds
#square_root
#identity
A \(3+\sqrt{10}\)
B \(5+\sqrt{6}\)
C \(\sqrt{10}+2\)
D \(4+\sqrt{3}\)
Explanation opens after your attempt
Correct Answer
A. \(3+\sqrt{10}\)
Step 1
Concept
Because (\(3+\sqrt{10}\)^{2}=9+10+6\sqrt{10}=19+6\sqrt{10}), \(\sqrt{A}=3+\sqrt{10}\). In exams, identify perfect-square surd forms.
Step 2
Why this answer is correct
The correct answer is A. \(3+\sqrt{10}\). Because (\(3+\sqrt{10}\)^{2}=9+10+6\sqrt{10}=19+6\sqrt{10}), \(\sqrt{A}=3+\sqrt{10}\). In exams, identify perfect-square surd forms.
Step 3
Exam Tip
क्योंकि (\(3+\sqrt{10}\)^{2}=9+10+6\sqrt{10}=19+6\sqrt{10}), इसलिए \(\sqrt{A}=3+\sqrt{10}\)। परीक्षा में पूर्ण वर्ग करणी पहचानें।
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