100 results found for "square-root-line" in Class 10.
In which equation is (x=0) one root and the other root negative?
A. \(x^2+7x=0\)
(x-2+7x=x(x+7)), इसलिए मूल (0) और (-7) हैं। दूसरा मूल ऋणात्मक है। / (x-2+7x=x(x+7)), so the roots are (0) and (-7). The other root is negative.
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In which equation is (x=0) one root and the other root positive?
A. \(x^2-6x=0\)
(x-2-6x=x(x-6)), इसलिए मूल (0) और (6) हैं। दूसरा मूल धनात्मक है। / (x-2-6x=x(x-6)), so the roots are (0) and (6). The other root is positive.
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Which square root is rational, so an irrationality proof like \(\sqrt{2}\) does not apply to it?
C. \(\sqrt{4}\)
(4) पूर्ण वर्ग है। / (4) is a perfect square.
\(\sqrt{4}=2\), जो परिमेय संख्या है। / \(\sqrt{4}=2\), which is rational.
पूर्ण वर्गों के वर्गमूल परिमेय होते हैं। / Square roots of perfect squares are rational.
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Which square root is not an example of irrationality proof in this chapter because it is rational?
A. \(\sqrt{9}\)
(9) पूर्ण वर्ग है। / (9) is a perfect square.
\(\sqrt{9}=3\), जो परिमेय है। / \(\sqrt{9}=3\), which is rational.
पूर्ण वर्ग के वर्गमूल को अपरिमेय सिद्ध करने की जरूरत नहीं होती। / A square root of a perfect square does not need an irrationality proof.
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A. \(\sqrt{4}\)
(4) पूर्ण वर्ग है। / (4) is a perfect square.
\(\sqrt{4}=2\), जो परिमेय संख्या है। / \(\sqrt{4}=2\), which is rational.
पूर्ण वर्ग के वर्गमूल को अपरिमेय सिद्ध नहीं करते। / The square root of a perfect square is not proved irrational.
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If \( \sqrt{x}=7.9 \), with which point is (x) associated on the number line?
C. (62.41)
\(x=7.9^2=62.41\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें। / \(x=7.9^2=62.41\). Square both sides to remove the square root.
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If \( \sqrt{x}=6.8 \), with which point is (x) associated on the number line?
C. (46.24)
\(x=6.8^2=46.24\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें। / \(x=6.8^2=46.24\). Square both sides to remove the square root.
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If \( \sqrt{x}=4.7 \), then (x) corresponds to which value on the number line?
C. (22.09)
\(x=4.7^2=22.09\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें। / \(x=4.7^2=22.09\). Square both sides to remove the square root.
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If \( \sqrt{x}=3.9 \), with which point is (x) associated on the number line?
A. (15.21)
\(x=3.9^2=15.21\) है। वर्गमूल हटाने के लिए दोनों पक्षों का वर्ग करें। / \(x=3.9^2=15.21\). Square both sides to remove the square root.
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Which number is equal to \(\sqrt{9.61}\) on the number line?
A. (3.1)
क्योंकि \(3.1^2=9.61\), इसलिए \(\sqrt{9.61}=3.1\)। दशमलव वर्गों को सावधानी से गुणा करें। / Because \(3.1^2=9.61\), \(\sqrt{9.61}=3.1\). Multiply decimal squares carefully.
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What is the correct position of \(\sqrt{0.49}\) on the number line?
B. (0.7)
\(0.7^2=0.49\), इसलिए \(\sqrt{0.49}=0.7\) है। दशमलव वर्गों में स्थान मान सावधानी से देखें। / Since \(0.7^2=0.49\), \(\sqrt{0.49}=0.7\). Be careful with place value in decimal squares.
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On the number line \(\sqrt{9}\) is the same as which point?
B. (3)
\(\sqrt{9}=3\), इसलिए यह बिंदु (3) पर होगा। पूर्ण वर्गों के वर्गमूल तुरंत पहचानें। / \(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.
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What is the position of \(\sqrt{16}\) on the number line?
A. (4)
\(\sqrt{16}=4\), इसलिए इसका स्थान (4) है। पूर्ण वर्गों के वर्गमूल सीधे पहचाने जा सकते हैं। / \(\sqrt{16}=4\), so its position is (4). Square roots of perfect squares can be identified directly.
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Which number is equal to \(\sqrt{9}\) on the number line?
A. (3)
\(\sqrt{9}=3\), इसलिए यह (3) के बिंदु पर होगा। वर्गमूल का मुख्य मान धनात्मक लिया जाता है। / \(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
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Which of the following is not a perfect square and its square root is proved irrational?
A. (2)
(4), (9) और (25) पूर्ण वर्ग हैं। / (4), (9), and (25) are perfect squares.
(2) पूर्ण वर्ग नहीं है, इसलिए \(\sqrt{2}\) अपरिमेय सिद्ध किया जाता है। / (2) is not a perfect square, so \(\sqrt{2}\) is proved irrational.
पूर्ण वर्ग और अपूर्ण वर्ग की पहचान पहले करें। / First identify perfect and non-perfect squares.
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On the number line, \( -\sqrt{2.56} \) is equal to which point?
A. ( -1.6 )
\( \sqrt{2.56}=1.6 \), इसलिए \( -\sqrt{2.56}=-1.6 \)। बाहर के ऋण चिह्न को अलग से संभालें। / \( \sqrt{2.56}=1.6 \), so \( -\sqrt{2.56}=-1.6 \). Handle the outside negative sign separately.
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On the number line, \( -\sqrt{1.69} \) is equal to which point?
A. ( -1.3 )
\( \sqrt{1.69}=1.3 \), इसलिए \( -\sqrt{1.69}=-1.3 \)। बाहर के ऋण चिह्न को अलग से संभालें। / \( \sqrt{1.69}=1.3 \), so \( -\sqrt{1.69}=-1.3 \). Handle the outside negative sign separately.
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On the number line, \( -\sqrt{0.36} \) is equal to which point?
A. ( -0.6 )
\( \sqrt{0.36}=0.6 \) है इसलिए \( -\sqrt{0.36}=-0.6 \)। बाहर के ऋण चिह्न को अलग से देखें। / \( \sqrt{0.36}=0.6 \), so \( -\sqrt{0.36}=-0.6 \). Treat the outside negative sign separately.
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What roots are obtained by solving \(7x^2=175\) by square root method?
A. \(x=\pm5\)
पहले \(x^2=25\) मिलता है, इसलिए \(x=\pm5\) है। परीक्षा में वर्गमूल लेते समय दोनों चिन्ह लिखें। / First \(x^2=25\), so \(x=\pm5\). In exams, write both signs while taking square root.
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What roots are obtained by solving \(5x^2=80\) by square root method?
A. \(x=\pm4\)
पहले \(x^2=16\) मिलता है, इसलिए \(x=\pm4\) है। परीक्षा में वर्गमूल लेते समय दोनों चिन्ह लिखें। / First \(x^2=16\), so \(x=\pm4\). In exams, write both signs while taking square root.
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What roots are obtained by solving \(3x^2=12\) by square root method?
A. \(x=\pm2\)
पहले \(x^2=4\) मिलता है, इसलिए \(x=\pm2\) है। परीक्षा में वर्गमूल लेते समय दोनों चिन्ह लिखें। / First \(x^2=4\), so \(x=\pm2\). In exams, write both signs while taking square root.
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Solving \(x^2=169\) by square root method gives what?
A. \(x=\pm13\)
\(x=\pm\sqrt{169}=\pm13\) होता है। परीक्षा में केवल (13) लिखना अधूरा उत्तर है। / \(x=\pm\sqrt{169}=\pm13\). In exams, writing only (13) is an incomplete answer.
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By square root method, what are the solutions of \(x^2=144\)?
A. \(x=\pm12\)
\(x=\pm\sqrt{144}=\pm12\) होता है। परीक्षा में वर्गमूल लेते समय \(\pm\) लगाना न भूलें। / \(x=\pm\sqrt{144}=\pm12\). In exams, do not forget \(\pm\) while taking square root.
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Solving \(x^2=121\) by square root method gives what?
A. \(x=\pm11\)
\(x=\pm\sqrt{121}=\pm11\) होता है। परीक्षा में केवल (11) लिखना अधूरा उत्तर है। / \(x=\pm\sqrt{121}=\pm11\). In exams, writing only (11) is an incomplete answer.
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By square root method, what are the solutions of \(x^2=64\)?
A. \(x=\pm8\)
\(x=\pm\sqrt{64}=\pm8\) होता है। परीक्षा में वर्गमूल लेते समय दोनों चिन्ह लिखें। / \(x=\pm\sqrt{64}=\pm8\). In exams, write both signs while taking square root.
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Which equation can be solved directly by square root method?
A. ((x-2)2=9)
((x-2)2=9) में सीधे वर्गमूल लिया जा सकता है। परीक्षा में ((expression)2=k) रूप को पहचानें। \(/ In ((x-2)^2=9), square root can be taken directly. In exams, recognize the form ((\)expression\()^2=k).\)
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Solving \(x^2=49\) by square root method gives what?
A. \(x=\pm7\)
\(x=\pm\sqrt{49}=\pm7\) होता है। परीक्षा में केवल धनात्मक मूल लिखना सामान्य गलती है। / \(x=\pm\sqrt{49}=\pm7\). In exams, writing only the positive root is a common mistake.
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If \(x^2=16\), what is the value of (x) by square root method?
A. \(x=\pm4\)
\(x^2=16\) से \(x=\pm\sqrt{16}=\pm4\) मिलता है। परीक्षा में वर्गमूल लेते समय \(\pm\) लगाना न भूलें। / From \(x^2=16\), \(x=\pm\sqrt{16}=\pm4\). In exams, do not forget \(\pm\) while taking square root.
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If \(a=7+4\sqrt{3}\), which option represents a square root of (a)?
A. \(2+\sqrt{3}\)
(\(2+\sqrt{3}\)2=4+4\sqrt{3}+3)। / (\(2+\sqrt{3}\)2=4+4\sqrt{3}+3).
यह \(7+4\sqrt{3}\) के बराबर है। / This equals \(7+4\sqrt{3}\).
ऐसे प्रश्नों में \(m+n+2\sqrt{mn}\) का रूप पहचानें। / In such questions, identify the form \(m+n+2\sqrt{mn}\).
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What is the square root of \(2^6 \times 5^2\)?
B. \(2^3 \times 5\)
वर्गमूल लेते समय अभाज्य घातों को आधा करते हैं। / When taking a square root, halve the prime exponents.
\(2^6\) से \(2^3\) और \(5^2\) से (5) मिलता है। / \(2^6\) becomes \(2^3\), and \(5^2\) becomes (5).
वर्गमूल में आधार नहीं बदलता, घात आधी होती है। / In square roots, the base does not change; the exponent is halved.
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What is the square root of \(2^4 \times 3^2\)?
A. \(2^2 \times 3\)
वर्गमूल लेते समय सभी अभाज्य घातों को आधा करते हैं। / When taking a square root, halve all prime exponents.
\(2^4\) से \(2^2\) और \(3^2\) से (3) मिलता है। / \(2^4\) becomes \(2^2\) and \(3^2\) becomes (3).
वर्गमूल में आधार को नहीं, घात को आधा करें। / In square roots, halve the exponent, not the base.
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If a number has prime factorisation \(2^6\times3^4\times5^2\), what is its square root?
A. \(2^3\times3^2\times5\)
वर्गमूल लेते समय हर अभाज्य गुणनखंड की घात आधी हो जाती है। / In square root, each prime exponent becomes half.
\(2^6\) से \(2^3\), \(3^4\) से \(3^2\), और \(5^2\) से (5) मिलेगा। / \(2^6\) becomes \(2^3\), \(3^4\) becomes \(3^2\), and \(5^2\) becomes (5).
यह विधि तभी सीधे लागू होती है जब सभी घातें सम हों। / This direct method works when all exponents are even.
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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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If \(x=\sqrt{a}\) and (12.6<x<12.7) on the number line, which value of (a) is correct?
B. (159)
\(12.6^2=158.76\) और \(12.7^2=161.29\), इसलिए (a) इनके बीच होना चाहिए। (159) सही है। / \(12.6^2=158.76\) and \(12.7^2=161.29\), so (a) must lie between them. (159) is correct.
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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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At which point will \( \sqrt{7.84} \) be marked on the number line?
C. (2.8)
\(2.8^2=7.84\), इसलिए \( \sqrt{7.84}=2.8 \)। दशमलव वर्गमूल में स्थानमान सावधानी से देखें। / Since \(2.8^2=7.84\), \( \sqrt{7.84}=2.8 \). Watch place value carefully in decimal square 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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If \(x=\sqrt{a}\) and (11.3<x<11.4) on the number line, which value of (a) is correct?
C. (128)
\(11.3^2=127.69\) और \(11.4^2=129.96\), इसलिए (a) इनके बीच होना चाहिए। (128) सही है। / \(11.3^2=127.69\) and \(11.4^2=129.96\), so (a) must lie between them. (128) is correct.
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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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At which point will \( \sqrt{5.76} \) be marked on the number line?
C. (2.4)
\(2.4^2=5.76\), इसलिए \( \sqrt{5.76}=2.4 \)। दशमलव वर्गों का स्थानमान ध्यान से देखें। / Since \(2.4^2=5.76\), \( \sqrt{5.76}=2.4 \). Watch place value in decimal squares.
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On the number line, \( \sqrt{\frac{81}{196}} \) is equal to which point?
A. \( \frac{9}{14} \)
\( \sqrt{\frac{81}{196}}=\frac{9}{14} \) है। अंश और हर दोनों का धनात्मक वर्गमूल लें। / \( \sqrt{\frac{81}{196}}=\frac{9}{14} \). Take the positive square root of both numerator and denominator.
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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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On the number line, \( \sqrt{3.24} \) is equal to which point?
B. (1.8)
\(1.8^2=3.24\), इसलिए \( \sqrt{3.24}=1.8 \)। दशमलव वर्गों में स्थानमान सावधानी से देखें। / Since \(1.8^2=3.24\), \( \sqrt{3.24}=1.8 \). Check place value carefully in decimal squares.
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If \(x=-\sqrt{29}\) on the number line, in which interval will (x) lie?
B. ( -6 ) और ( -5 ) के बीचBetween ( -6 ) and ( -5 )
क्योंकि \(5<\sqrt{29}<6\), इसलिए \(-6<-\sqrt{29}<-5\)। ऋणात्मक मूलों में क्रम उलटकर लिखें। / Since \(5<\sqrt{29}<6\), \(-6<-\sqrt{29}<-5\). For negative roots, write the reversed interval carefully.
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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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If \(x=\sqrt{a}\) and (5.2<x<5.3) on the number line, which value of (a) is correct?
A. (28)
\(5.2^2=27.04\) और \(5.3^2=28.09\), इसलिए (a) इनके बीच होना चाहिए। (28) सही है। / \(5.2^2=27.04\) and \(5.3^2=28.09\), so (a) must lie between them. (28) is correct.
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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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At which point will \( \sqrt{2.89} \) be marked on the number line?
A. (1.7)
\(1.7^2=2.89\) इसलिए \( \sqrt{2.89}=1.7 \)। दशमलव वर्ग पहचानना समय बचाता है। / Since \(1.7^2=2.89\), \( \sqrt{2.89}=1.7 \). Recognising decimal squares saves time.
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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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On the number line, \( \sqrt{\frac{25}{16}} \) is equal to which point?
A. \( \frac{5}{4}\)
\( \sqrt{\frac{25}{16}}=\frac{5}{4}\) क्योंकि धनात्मक वर्गमूल लिया जाता है। भिन्न के वर्गमूल में अंश और हर दोनों का मूल लें। / \( \sqrt{\frac{25}{16}}=\frac{5}{4}\) because the principal square root is positive. Take the root of both numerator and denominator.
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A. (-7) और (-6)(-7) and (-6)
\(6<\sqrt{48}<7\), इसलिए \(-7<-\sqrt{48}<-6\)। ऋणात्मक वर्गमूल में अंतराल उल्टा लिखें। / Since \(6<\sqrt{48}<7\), \(-7<-\sqrt{48}<-6\). Write the interval carefully for negative 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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Which legs of a right triangle are most suitable to construct \(\sqrt{17}\) on the number line?
A. (4) और (1)(4) and (1)
क्योंकि \(4^2+1^2=17\), इसलिए कर्ण \(\sqrt{17}\) होगा। संख्या रेखा पर वर्गमूल निर्माण में पाइथागोरस प्रमेय उपयोगी है। / Because \(4^2+1^2=17\), the hypotenuse will be \(\sqrt{17}\). Pythagoras theorem is useful for square-root construction on the number line.
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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 statement justifies \(0<\sqrt{0.49}<1\) on the number line?
A. क्योंकि (0<0.49<1)Because (0<0.49<1)
यदि (0<a<1), तो \(0<\sqrt{a}<1\); यहाँ (a=0.49) है। दशमलव वर्गमूलों में सीमा पहले पहचानें। / If (0<a<1), then \(0<\sqrt{a}<1\); here (a=0.49). For decimal square roots, identify the bounds first.
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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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On the number line, \(\sqrt{45}\) will be closest to which integer?
C. (7)
\(\sqrt{45}\) लगभग (6.7) है इसलिए यह (7) के अधिक पास है। अनुमान में पास के पूर्ण वर्ग (36) और (49) उपयोगी हैं। / \(\sqrt{45}\) is about (6.7), so it is closer to (7). Nearby perfect squares (36) and (49) help in estimation.
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What is the distance between \(-\sqrt{16}\) and (2.5) on the number line?
C. (6.5)
\(-\sqrt{16}=-4\), इसलिए दूरी (|2.5-(-4)|=6.5) है। दूरी हमेशा धनात्मक लेते हैं। / \(-\sqrt{16}=-4\), so the distance is (|2.5-(-4)|=6.5). Distance is always taken positive.
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Between which two consecutive integers will \(\sqrt{26}\) lie on the number line?
B. (5) और (6)(5) and (6)
क्योंकि \(5^2<26<6^2\), इसलिए \(\sqrt{26}\) (5) और (6) के बीच होगा। पास के पूर्ण वर्ग देखें। / Since \(5^2<26<6^2\), \(\sqrt{26}\) lies between (5) and (6). Check nearby perfect squares.
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B. \(\sqrt{17}\)
कर्ण \(=\sqrt{4^2+1^2}=\sqrt{17}\) होगा। ऐसी रचना में पाइथागोरस प्रमेय लगाएं। / The hypotenuse is \(\sqrt{4^2+1^2}=\sqrt{17}\). Use Pythagoras in this type of construction.
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Between which two integers will \(\sqrt{27}\) lie on the number line?
C. (5) और (6)(5) and (6)
क्योंकि \(5^2=25\) और \(6^2=36\), इसलिए \(\sqrt{27}\) (5) और (6) के बीच है। परीक्षा में निकट पूर्ण वर्गों को याद रखें। / Since \(5^2=25\) and \(6^2=36\), \(\sqrt{27}\) lies between (5) and (6). In exams, remember nearby perfect squares.
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Between which two integers will \(-\sqrt{18}\) lie on the number line?
C. (-5) और (-4)(-5) and (-4)
क्योंकि \(\sqrt{18}\) (4) और (5) के बीच है, इसलिए \(-\sqrt{18}\) (-5) और (-4) के बीच होगा। परीक्षा में ऋणात्मक वर्गमूल में दिशा उलटी हो जाती है। / Since \(\sqrt{18}\) lies between (4) and (5), \(-\sqrt{18}\) lies between (-5) and (-4). In exams, the direction reverses for negative square roots.
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Between which two integers will \(\sqrt{10}\) be correctly represented on the number line?
B. (3) और (4)(3) and (4)
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। / Since \(3^2=9\) and \(4^2=16\), \(\sqrt{10}\) lies between (3) and (4). In exams, bracket square roots between perfect squares.
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Which relation between \(\sqrt{8}\) and (3) on the number line is correct?
C. \(\sqrt{8}<3\)
क्योंकि (8<9), इसलिए \(\sqrt{8}<3\) है। तुलना के लिए दोनों ओर वर्ग सोचें। / Since (8<9), \(\sqrt{8}<3\). For comparison, think in terms of squares.
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C. यह (3) और (4) के बीच होगाIt will be between (3) and (4)
क्योंकि \(3^2<12<4^2\), इसलिए \(\sqrt{12}\) (3) और (4) के बीच है। वर्गमूल संख्या को छोटा कर सकता है। / Since \(3^2<12<4^2\), \(\sqrt{12}\) lies between (3) and (4). A square root can be much smaller than the number.
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For \(\sqrt{a^2}\) on the number line, if (a=-4), which point will it be?
B. (4)
\(\sqrt{a^2}=|a|\), इसलिए (a=-4) पर मान (4) होगा। वर्गमूल का मुख्य मान ऋणात्मक नहीं होता। / \(\sqrt{a^2}=|a|\), so for (a=-4) the value is (4). The principal square root is not negative.
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Which statement is true: on the number line, which is to the right, \(\sqrt{2}\) or \(\sqrt{3}\)?
B. \(\sqrt{3}\) दाईं ओर है\(\sqrt{3}\) is to the right
क्योंकि (3>2), इसलिए \(\sqrt{3}>\sqrt{2}\) है। धनात्मक वर्गमूलों में बड़ी संख्या का वर्गमूल बड़ा होता है। / Since (3>2), \(\sqrt{3}>\sqrt{2}\). For positive square roots, the root of the larger number is larger.
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On the number line, \(\sqrt{20}\) is closest to which integer?
B. (4)
\(\sqrt{20}\) लगभग (4.47) है इसलिए यह (4) के अधिक पास है। \(\sqrt{20}\) को (4) और (5) के बीच रखकर दूरी सोचें। / \(\sqrt{20}\) is about (4.47), so it is closer to (4). Place \(\sqrt{20}\) between (4) and (5) and compare distances.
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Which is the most accurate estimate of \(\sqrt{3}\) on the number line?
B. (1.7)
\(\sqrt{3}\) लगभग (1.732) है इसलिए (1.7) सबसे पास है। अनुमान के लिए \(\sqrt{3}\) को (1) और (2) के बीच रखें। / \(\sqrt{3}\) is about (1.732), so (1.7) is closest. For estimation place \(\sqrt{3}\) between (1) and (2).
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C. (25<a<36)
\(5<\sqrt{a}<6\) होने पर (25<a<36) होगा। वर्गमूल की सीमा को वर्ग करके (a) की सीमा मिलती है। / If \(5<\sqrt{a}<6\), then (25<a<36). Square the root bounds to get the range of (a).
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Which integer is closest to \(\sqrt{18}\) on the number line?
B. (4)
\(\sqrt{18}\) लगभग (4.24) है इसलिए यह (4) के अधिक पास है। अनुमान के लिए पास के पूर्ण वर्ग (16) और (25) देखें। / \(\sqrt{18}\) is about (4.24), so it is closer to (4). For estimation, check nearby perfect squares (16) and (25).
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If \(\sqrt{n}\) lies between (4) and (5) on the number line, which value of (n) is possible?
C. (21)
\(\sqrt{n}\) के (4) और (5) के बीच होने के लिए (16<n<25) चाहिए। दिए गए विकल्पों में (21) सही है। / For \(\sqrt{n}\) to lie between (4) and (5), (16<n<25) is needed. Among the options (21) is correct.
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Which statement about the position of \(\sqrt{7}\) on the number line is correct?
B. यह (2) और (3) के बीच हैIt is between (2) and (3)
क्योंकि \(2^2<7<3^2\), इसलिए \(\sqrt{7}\), (2) और (3) के बीच होगा। \(\sqrt{7}\) को (7) समझना सामान्य गलती है। / Since \(2^2<7<3^2\), \(\sqrt{7}\) lies between (2) and (3). Taking \(\sqrt{7}\) as (7) is a common mistake.
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Which statement gives the correct position of \(-\sqrt{4}\) on the number line?
B. यह (-2) पर होगाIt will be at (-2)
\(\sqrt{4}=2\), इसलिए \(-\sqrt{4}=-2\) होगा। ऋण चिह्न को वर्गमूल लेने के बाद भी याद रखें। / \(\sqrt{4}=2\), so \(-\sqrt{4}=-2\). Remember the negative sign after finding the square root.
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C. \(\sqrt{13}\)
कर्ण \(=\sqrt{3^2+2^2}=\sqrt{13}\) होता है। समकोण त्रिभुज में पाइथागोरस प्रमेय लागू करें। / The hypotenuse is \(\sqrt{3^2+2^2}=\sqrt{13}\). Apply Pythagoras in a right triangle.
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Between which two consecutive integers will \(\sqrt{10}\) be located on the number line?
B. (3) और (4)(3) and (4)
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। / Since \(3^2<10<4^2\), \(\sqrt{10}\) lies between (3) and (4). Use nearby perfect squares to locate roots.
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Which fact can be used to place \(\sqrt{5}\) correctly on the number line?
A. \(2^2<5<3^2\)
क्योंकि (4<5<9), इसलिए \(\sqrt{5}\), (2) और (3) के बीच होगा। वर्गों की तुलना से वर्गमूल की स्थिति मिलती है। / Since (4<5<9), \(\sqrt{5}\) lies between (2) and (3). Comparing squares helps locate square roots.
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B. \(\sqrt{2}\)
पाइथागोरस से कर्ण \(=\sqrt{1^2+1^2}=\sqrt{2}\) होगा। ऐसी रचनाओं में वर्गों का योग जरूर देखें। / By Pythagoras the hypotenuse is \(\sqrt{1^2+1^2}=\sqrt{2}\). In such constructions always add the squares of perpendicular sides.
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On the number line, which point will be to the right, \(\sqrt{2}\) or \(\sqrt{8}\)?
B. \(\sqrt{8}\)
क्योंकि (8>2), इसलिए \(\sqrt{8}>\sqrt{2}\) है। परीक्षा में धनात्मक वर्गमूलों की तुलना अंदर की संख्या से करें। / Since (8>2), \(\sqrt{8}>\sqrt{2}\). In exams, compare positive square roots using the numbers inside them.
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Between which two consecutive integers will \(\sqrt{5}\) lie on the number line?
B. (2) और (3)(2) and (3)
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\), (2) और (3) के बीच होगा। वर्गों से वर्गमूल की स्थिति जल्दी मिलती है। / Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3). Use squares to locate square roots quickly.
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Between which two integers does \(\sqrt{13}\) lie on the number line?
A. (3) और (4)(3) and (4)
क्योंकि \(3^2<13<4^2\), इसलिए \(\sqrt{13}\), (3) और (4) के बीच है। वर्गों से तुलना आसान होती है। / Since \(3^2<13<4^2\), \(\sqrt{13}\) lies between (3) and (4). Comparing squares makes it easy.
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Between which two integers does \(\sqrt{8}\) lie on the number line?
A. (2) और (3)(2) and (3)
क्योंकि \(2^2<8<3^2\), इसलिए \(\sqrt{8}\), (2) और (3) के बीच है। पहले पास के पूर्ण वर्ग पहचानें। / Since \(2^2<8<3^2\), \(\sqrt{8}\) lies between (2) and (3). First identify nearby perfect squares.
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Between which two integers does \(\sqrt{10}\) lie on the number line?
A. (3) और (4)(3) and (4)
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। / Since \(3^2<10<4^2\), \(\sqrt{10}\) lies between (3) and (4). Always place (n) between nearby perfect squares.
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