square root se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
174 questions tagged with square root.
On the number line, \( \sqrt{156} \) is closest to which integer?
B. (12)
\( \sqrt{156}\approx12.49 \), इसलिए यह (12) के थोड़ा अधिक निकट है। निकटतम पूर्णांक के लिए दूरी जाँचें। / \( \sqrt{156}\approx12.49 \), so it is slightly closer to (12). Check distance for the nearest integer.
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Which option gives the correct decimal bound for \( \sqrt{86} \) on the number line?
B. \(9.2<\sqrt{86}<9.3\)
\(9.2^2=84.64\) और \(9.3^2=86.49\), इसलिए \( \sqrt{86} \) इनके बीच है। दशमलव सीमा के लिए वर्ग जाँचें। / \(9.2^2=84.64\) and \(9.3^2=86.49\), so \( \sqrt{86} \) lies between them. Check squares for decimal bounds.
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Which decimal value is closest to \( \sqrt{199} \) on the number line?
A. (14.10)
\( \sqrt{199}\approx14.11 \), इसलिए (14.10) सबसे निकट है। बड़े मूलों में निकट वर्गों से जाँच करें। / \( \sqrt{199}\approx14.11 \), so (14.10) is closest. Check nearby squares for large roots.
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On the number line, \( \sqrt{132} \) is closest to which integer?
B. (11)
\( \sqrt{132}\approx11.49 \), इसलिए यह (11) के थोड़ा अधिक निकट है। निकटतम पूर्णांक के लिए दूरी जाँचें। / \( \sqrt{132}\approx11.49 \), so it is slightly closer to (11). Check distance for the nearest integer.
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Which option gives the correct decimal bound for \( \sqrt{57} \) on the number line?
B. \(7.5<\sqrt{57}<7.6\)
\(7.5^2=56.25\) और \(7.6^2=57.76\), इसलिए \( \sqrt{57} \) इनके बीच है। दशमलव सीमा के लिए वर्ग जाँचें। / \(7.5^2=56.25\) and \(7.6^2=57.76\), so \( \sqrt{57} \) lies between them. Check squares for decimal bounds.
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Which decimal value is closest to \( \sqrt{143} \) on the number line?
A. (11.96)
\( \sqrt{143}\approx11.96 \) क्योंकि \(11.96^2\) लगभग (143) है। बड़े मूलों में निकट वर्गों से जाँच करें। / \( \sqrt{143}\approx11.96 \) because \(11.96^2\) is close to (143). Check nearby squares for large roots.
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On the number line, \( \sqrt{98} \) is closest to which integer?
C. (10)
\( \sqrt{98}\approx9.899 \), इसलिए यह (10) के सबसे निकट है। निकटतम पूर्णांक के लिए दूरी देखें। / \( \sqrt{98}\approx9.899 \), so it is closest to (10). Check distance for the nearest integer.
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Which option gives the correct decimal bound for \( \sqrt{30} \)?
B. \(5.4<\sqrt{30}<5.5\)
\(5.4^2=29.16\) और \(5.5^2=30.25\), इसलिए \( \sqrt{30} \) इनके बीच है। दशमलव सीमा के लिए वर्ग जाँचें। / \(5.4^2=29.16\) and \(5.5^2=30.25\), so \( \sqrt{30} \) lies between them. Check squares for decimal bounds.
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On the number line, \( \sqrt{90} \) is closest to which integer?
B. (10)
\( \sqrt{90}\approx9.49 \) है जो (9) की तुलना में (10) के अधिक निकट है। निकटतम पूर्णांक के लिए दूरी जाँचें। / \( \sqrt{90}\approx9.49 \), which is closer to (10) than to (9). Check distance for the nearest integer.
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Which option gives the correct decimal bound for \( \sqrt{24} \) on the number line?
A. \(4.8<\sqrt{24}<4.9\)
\(4.8^2=23.04\) और \(4.9^2=24.01\) है। इसलिए \( \sqrt{24} \) इनके बीच है। / \(4.8^2=23.04\) and \(4.9^2=24.01\). Hence \( \sqrt{24} \) lies between them.
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Which decimal value is closest to \( \sqrt{63} \) on the number line?
A. (7.94)
\( \sqrt{63}\approx7.94 \) क्योंकि \(7.94^2\) लगभग (63) है। बड़े मूलों में निकट वर्ग जाँचें। / \( \sqrt{63}\approx7.94 \) because \(7.94^2\) is close to (63). Check nearby squares for large roots.
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If \(A=\sqrt{14}\) and (B=4) on the number line, which value lies between (A) and (B)?
A. (3.8)
\( \sqrt{14}\approx3.742\), इसलिए (3.8) इसके और (4) के बीच है। निकट वर्गमूलों में दशमलव अनुमान जरूरी है। / \( \sqrt{14}\approx3.742\), so (3.8) lies between it and (4). Decimal estimation is important for nearby square roots.
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A. \( \sqrt{1^2+1^2}\)
समकोण त्रिभुज में भुजाएँ (1) और (1) लेने पर कर्ण \( \sqrt{2}\) होता है। पायथागोरस प्रमेय से निर्माण समझें। / With perpendicular sides (1) and (1), the hypotenuse is \( \sqrt{2}\). Understand the construction using Pythagoras theorem.
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If (x) lies between (2.6) and (2.7), which test is correct for \(x=\sqrt{7}\)?
A. \(2.6^2<7<2.7^2\)
\(2.6^2=6.76\) और \(2.7^2=7.29\), इसलिए \(\sqrt{7}\) इनके बीच है। अनुमान को वर्ग करके जाँचें। / \(2.6^2=6.76\) and \(2.7^2=7.29\), so \(\sqrt{7}\) lies between them. Check an estimate by squaring.
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If \(\sqrt{n}\) lies between (5) and (6) on the number line, which value of (n) is possible?
A. (30)
\(5<\sqrt{n}<6\) से (25<n<36), इसलिए (30) संभव है। वर्गमूल असमानता में धनात्मक पक्षों का वर्ग लें। / From \(5<\sqrt{n}<6\), we get (25<n<36), so (30) is possible. Square positive sides in square-root inequalities.
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Which number is closest to \(\sqrt{6}\) on the number line?
A. (2.45)
\(\sqrt{6}\approx2.449\), इसलिए (2.45) सबसे निकट है। निकटता के लिए अनुमानित मान से अंतर जाँचें। / \(\sqrt{6}\approx2.449\), so (2.45) is closest. To test closeness, compare differences from the approximate value.
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Which option gives the correct interval for \(\sqrt{20}\) on the number line?
A. ((4,5))
क्योंकि \(4^2=16\) और \(5^2=25\), इसलिए \(4<\sqrt{20}<5\)। पूर्ण वर्गों की सीमा तुरंत अंतराल देती है। / Because \(4^2=16\) and \(5^2=25\), \(4<\sqrt{20}<5\). Perfect-square bounds quickly give the interval.
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If \(\sqrt{10}\) is placed on the number line, between which two integers will it lie?
A. (3) और (4)(3) and (4)
क्योंकि \(3^2=9\) और \(4^2=16\), इसलिए \(3<\sqrt{10}<4\)। पहले निकटतम पूर्ण वर्ग खोजें। / Because \(3^2=9\) and \(4^2=16\), \(3<\sqrt{10}<4\). First find the nearest perfect squares.
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A. \(1.4<\sqrt{2}<1.5\)
क्योंकि \(1.4^2=1.96\) और \(1.5^2=2.25\), इसलिए \(\sqrt{2}\) इनके बीच है। कठिन प्रश्नों में दशमलव के वर्ग का प्रयोग करें। / Because \(1.4^2=1.96\) and \(1.5^2=2.25\), \(\sqrt{2}\) lies between them. For hard questions, use squares of decimals.
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Between which two integers will \(\sqrt{37}-6\) lie on the number line?
A. (0) और (1)(0) and (1)
क्योंकि \(6^2<37<7^2\), इसलिए \(6<\sqrt{37}<7\) और \(0<\sqrt{37}-6<1\) है। वर्गमूल वाले अंतराल में समान संख्या घटाकर स्थिति पाएं। / Since \(6^2<37<7^2\), \(6<\sqrt{37}<7\) and \(0<\sqrt{37}-6<1\). Subtract the same number from a root interval to locate the value.
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Which statement about \(\sqrt{24}\) on the number line is false?
D. \(\sqrt{24}=24\)
क्योंकि \(4^2<24<5^2\), इसलिए \(\sqrt{24}\) (4) और (5) के बीच है और (24) के बराबर नहीं है। वर्गमूल को मूल संख्या न मानें। / Since \(4^2<24<5^2\), \(\sqrt{24}\) is between (4) and (5) and is not equal to (24). Do not treat a square root as the original number.
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Which of these values is closest to (2) on the number line?
B. \(\sqrt{5}\)
\(\sqrt{5}\approx2.24\), जो दिए गए विकल्पों में (2) के सबसे पास है। निकटता के लिए प्रत्येक दूरी की तुलना करें। / \(\sqrt{5}\approx2.24\), which is closest to (2) among the options. Compare each distance for closeness.
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What is the increasing order of \(\sqrt{1}\), \(\sqrt{2}\), and \(\sqrt{3}\) on the number line?
B. \(\sqrt{1},\sqrt{2},\sqrt{3}\)
धनात्मक संख्याओं के लिए (1<2<3) होने पर \(\sqrt{1}<\sqrt{2}<\sqrt{3}\) है। वर्गमूल क्रम को बनाए रखता है। / For positive numbers, (1<2<3) gives \(\sqrt{1}<\sqrt{2}<\sqrt{3}\). Square root preserves order.
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If \(\sqrt{a}\) is exactly at (4.5) on the number line, what will be the value of (a)?
C. (20.25)
\(\sqrt{a}=4.5\) होने पर (a=(4.5)2=20.25) है। वर्गमूल हटाने के लिए वर्ग करें। / If \(\sqrt{a}=4.5\), then (a=(4.5)2=20.25). Square both sides to remove the square root.
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What is the best decimal estimate of \(\sqrt{\frac{1}{2}}\) on the number line?
B. (0.707)
\(\sqrt{\frac{1}{2}}\approx0.707\) होता है। अनुमान में वर्ग करके विकल्प जांच सकते हैं। / \(\sqrt{\frac{1}{2}}\approx0.707\). In estimation, you can square the options to check.
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Which relation between \(\sqrt{15}\) and (4) is correct on the number line?
A. \(\sqrt{15}<4\)
क्योंकि (15<16), इसलिए \(\sqrt{15}<4\) है। तुलना के लिए पूर्ण वर्ग से मिलाएं। / Since (15<16), \(\sqrt{15}<4\). Compare using the nearby perfect square.
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On the number line, \(\sqrt{32}\) is closest to which integer?
C. (6)
\(\sqrt{32}\approx5.66\) है इसलिए यह (6) के अधिक पास है। निकटतम पूर्णांक के लिए दूरी की तुलना करें। / \(\sqrt{32}\approx5.66\), so it is closer to (6). Compare distances for the nearest integer.
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A. (5) और (2)(5) and (2)
\(5^2+2^2=29\), इसलिए कर्ण \(\sqrt{29}\) होगा। भुजाओं के वर्गों का योग जांचें। / \(5^2+2^2=29\), so the hypotenuse will be \(\sqrt{29}\). Check the sum of squares of the sides.
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If \(\sqrt{n}\) lies between (6) and (7) on the number line, which value of (n) is possible?
C. (40)
इसके लिए (36<n<49) होना चाहिए और (40) इसी सीमा में है। वर्गमूल की सीमा को वर्ग करके जांचें। / For this, (36<n<49) is needed, and (40) lies in this range. Square the root bounds to check.
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Between which two integers will \(\sqrt{50}\) be located on the number line?
C. (7) और (8)(7) and (8)
क्योंकि \(7^2<50<8^2\), इसलिए \(\sqrt{50}\) (7) और (8) के बीच है। पूर्ण वर्गों से अंतराल तय करें। / Since \(7^2<50<8^2\), \(\sqrt{50}\) lies between (7) and (8). Use perfect squares to decide the interval.
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