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The midpoint is \( \frac{\sqrt{2}+\sqrt{8}}{2}=\frac{\sqrt{2}+2\sqrt{2}}{2}=\frac{3\sqrt{2}}{2} \). Take the average of the two values for the midpoint.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{3\sqrt{2}}{2} \). The midpoint is \( \frac{\sqrt{2}+\sqrt{8}}{2}=\frac{\sqrt{2}+2\sqrt{2}}{2}=\frac{3\sqrt{2}}{2} \). Take the average of the two values for the midpoint.
Step 3
Exam Tip
मध्य बिंदु \( \frac{\sqrt{2}+\sqrt{8}}{2}=\frac{\sqrt{2}+2\sqrt{2}}{2}=\frac{3\sqrt{2}}{2} \) है। मध्य के लिए दोनों मानों का औसत लें।
\( \sqrt{300}=10\sqrt{3} \) and \( \sqrt{147}=7\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{3}\). \( \sqrt{300}=10\sqrt{3} \) and \( \sqrt{147}=7\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
Step 3
Exam Tip
\( \sqrt{300}=10\sqrt{3} \) और \( \sqrt{147}=7\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें।
B. ( -8 ) और ( -7 ) के बीच/Between ( -8 ) and ( -7 )
Step 1
Concept
\( -\sqrt{27}\approx-5.196 \), so \( -\sqrt{27}-3\approx-8.196 \). Therefore it lies between (-9) and (-8).
Step 2
Why this answer is correct
The correct answer is B. ( -8 ) और ( -7 ) के बीच / Between ( -8 ) and ( -7 ). \( -\sqrt{27}\approx-5.196 \), so \( -\sqrt{27}-3\approx-8.196 \). Therefore it lies between (-9) and (-8).
Step 3
Exam Tip
\( -\sqrt{27}-3\approx-8.196 \) नहीं, बल्कि \( -\sqrt{27}\approx-5.196 \) होने से योग लगभग (-8.196) है। इसलिए यह (-9) और (-8) के बीच है।
Adding like radicals gives \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29}=4\sqrt{29} \). Do not add the numbers inside radicals directly.
Step 2
Why this answer is correct
The correct answer is B. \(4\sqrt{29}\). Adding like radicals gives \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29}=4\sqrt{29} \). Do not add the numbers inside radicals directly.
Step 3
Exam Tip
समान मूलों को जोड़ने पर \( \sqrt{29}+\sqrt{29}+\sqrt{29}+\sqrt{29}=4\sqrt{29} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं।
\( \sqrt{18}\approx4.243 \) and \( \sqrt{17}\approx4.123 \), so the difference is about (0.12). The difference of nearby roots is small.
Step 2
Why this answer is correct
The correct answer is B. (0.12). \( \sqrt{18}\approx4.243 \) and \( \sqrt{17}\approx4.123 \), so the difference is about (0.12). The difference of nearby roots is small.
Step 3
Exam Tip
\( \sqrt{18}\approx4.243 \) और \( \sqrt{17}\approx4.123 \), इसलिए अंतर लगभग (0.12) है। पास-पास मूलों का अंतर छोटा होता है।
By checking carefully, \( -3.61<-\sqrt{13}\approx-3.606<-\frac{18}{5}=-3.6 \). For negative values, the smaller number comes first.
Step 2
Why this answer is correct
The correct answer is A. \( -3.61,-\frac{18}{5},-\sqrt{13} \). By checking carefully, \( -3.61<-\sqrt{13}\approx-3.606<-\frac{18}{5}=-3.6 \). For negative values, the smaller number comes first.
Step 3
Exam Tip
\( -3.61<-3.6<-\sqrt{13}\approx-3.606 \) का क्रम सावधानी से देखने पर \( -3.61,-\sqrt{13},-\frac{18}{5} \) सही होता है। ऋणात्मक मानों में छोटी संख्या पहले आती है।
\( \sqrt{3}\approx1.732 \), so \( \frac{a}{100} \) must be between (1.732) and (1.74). (a=173) gives (1.73), which is slightly smaller, so check the bound carefully.
Step 2
Why this answer is correct
The correct answer is B. (173). \( \sqrt{3}\approx1.732 \), so \( \frac{a}{100} \) must be between (1.732) and (1.74). (a=173) gives (1.73), which is slightly smaller, so check the bound carefully.
Step 3
Exam Tip
\( \sqrt{3}\approx1.732 \), इसलिए \( \frac{a}{100} \) को (1.732) और (1.74) के बीच होना चाहिए। (a=173) से (1.73) मिलता है जो थोड़ा छोटा है, इसलिए सीमा सावधानी से जाँचें।
\(5-\sqrt{11}\approx1.683\) and \( \frac{17}{10}=1.7 \). Therefore the first value is slightly smaller.
Step 2
Why this answer is correct
The correct answer is A. \(5-\sqrt{11}<\frac{17}{10}\). \(5-\sqrt{11}\approx1.683\) and \( \frac{17}{10}=1.7 \). Therefore the first value is slightly smaller.
Step 3
Exam Tip
\(5-\sqrt{11}\approx1.683\) और \( \frac{17}{10}=1.7 \) है। इसलिए पहला मान थोड़ा छोटा है।
The point on the left is negative and its distance is \( \sqrt{41} \). Therefore the number is \( -\sqrt{41} \).
Step 2
Why this answer is correct
The correct answer is B. \( -\sqrt{41} \). The point on the left is negative and its distance is \( \sqrt{41} \). Therefore the number is \( -\sqrt{41} \).
Step 3
Exam Tip
बाईं ओर का बिंदु ऋणात्मक होगा और दूरी \( \sqrt{41} \) है। इसलिए संख्या \( -\sqrt{41} \) है।
\( \sqrt{15}+\frac{1}{8}\approx3.998 \), so (3.95) is not greater than it. In this case no listed value satisfies the condition.
Step 2
Why this answer is correct
The correct answer is A. (3.95). \( \sqrt{15}+\frac{1}{8}\approx3.998 \), so (3.95) is not greater than it. In this case no listed value satisfies the condition.
Step 3
Exam Tip
\( \sqrt{15}+\frac{1}{8}\approx3.998 \), इसलिए (3.95) इससे बड़ा नहीं है। ऐसी स्थिति में कोई दिया विकल्प शर्त पूरी नहीं करता।
Moving \( \frac{13}{6} \) to the right of (-5) gives \( -5+\frac{13}{6}=-\frac{17}{6} \). Use the given interval to choose direction.
Step 2
Why this answer is correct
The correct answer is A. \( -\frac{17}{6} \). Moving \( \frac{13}{6} \) to the right of (-5) gives \( -5+\frac{13}{6}=-\frac{17}{6} \). Use the given interval to choose direction.
Step 3
Exam Tip
(-5) से दाईं ओर \( \frac{13}{6} \) जाने पर \( -5+\frac{13}{6}=-\frac{17}{6} \) मिलता है। दिए गए अंतराल से दिशा चुनें।
\(9.2^2=84.64\) and \(9.3^2=86.49\), so \( \sqrt{86} \) lies between them. Check squares for decimal bounds.
Step 2
Why this answer is correct
The correct answer is B. \(9.2<\sqrt{86}<9.3\). \(9.2^2=84.64\) and \(9.3^2=86.49\), so \( \sqrt{86} \) lies between them. Check squares for decimal bounds.
Step 3
Exam Tip
\(9.2^2=84.64\) और \(9.3^2=86.49\), इसलिए \( \sqrt{86} \) इनके बीच है। दशमलव सीमा के लिए वर्ग जाँचें।
Moving left gives \( \frac{11}{12}-\frac{5}{18}=\frac{23}{36} \). Subtract the distance according to direction.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{23}{36} \). Moving left gives \( \frac{11}{12}-\frac{5}{18}=\frac{23}{36} \). Subtract the distance according to direction.
Step 3
Exam Tip
बाईं ओर जाने पर \( \frac{11}{12}-\frac{5}{18}=\frac{23}{36} \) मिलता है। दिशा के अनुसार दूरी घटाएँ।
B. ( -6 ) और ( -5 ) के बीच/Between ( -6 ) and ( -5 )
Step 1
Concept
\( \sqrt{99}\approx9.95 \), so \(p\approx-5.95\). Hence it lies between (-6) and (-5).
Step 2
Why this answer is correct
The correct answer is B. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 ). \( \sqrt{99}\approx9.95 \), so \(p\approx-5.95\). Hence it lies between (-6) and (-5).
Step 3
Exam Tip
\( \sqrt{99}\approx9.95 \), इसलिए \(p\approx-5.95\) है। अतः यह (-6) और (-5) के बीच होगा।
\( -\frac{43}{11}\approx-3.909 \), so it lies between (-4) and (-3). Convert negative fractions to decimals.
Step 2
Why this answer is correct
The correct answer is C. ( -4 ) और ( -3 ) / ( -4 ) and ( -3 ). \( -\frac{43}{11}\approx-3.909 \), so it lies between (-4) and (-3). Convert negative fractions to decimals.
Step 3
Exam Tip
\( -\frac{43}{11}\approx-3.909 \), इसलिए यह (-4) और (-3) के बीच है। ऋणात्मक भिन्नों को दशमलव में बदलें।
This decimal is non-terminating and non-repeating, so it is irrational. Check whether the decimal pattern truly repeats or not.
Step 2
Why this answer is correct
The correct answer is B. अपरिमेय संख्या / Irrational number. This decimal is non-terminating and non-repeating, so it is irrational. Check whether the decimal pattern truly repeats or not.
Step 3
Exam Tip
यह दशमलव असांत और अनावर्ती है, इसलिए अपरिमेय है। दशमलव पैटर्न सच में दोहरता है या नहीं, यह जाँचें।
\( \sqrt{108}=6\sqrt{3} \) and \( \sqrt{48}=4\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{3}\). \( \sqrt{108}=6\sqrt{3} \) and \( \sqrt{48}=4\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
Step 3
Exam Tip
\( \sqrt{108}=6\sqrt{3} \) और \( \sqrt{48}=4\sqrt{3} \), इसलिए अंतर \(2\sqrt{3}\) है। समान मूलों को ही घटाएँ।
The midpoint is \( \frac{\frac{7}{15}+\frac{11}{15}}{2}=\frac{3}{5} \). Use the average of the two values for the midpoint.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{3}{5} \). The midpoint is \( \frac{\frac{7}{15}+\frac{11}{15}}{2}=\frac{3}{5} \). Use the average of the two values for the midpoint.
Step 3
Exam Tip
मध्य बिंदु \( \frac{\frac{7}{15}+\frac{11}{15}}{2}=\frac{3}{5} \) है। मध्य के लिए दोनों मानों का औसत लें।
Moving left means subtracting the distance, so the coordinate is \( -4-\sqrt{23} \). Choose the sign by direction.
Step 2
Why this answer is correct
The correct answer is C. \( -4-\sqrt{23} \). Moving left means subtracting the distance, so the coordinate is \( -4-\sqrt{23} \). Choose the sign by direction.
Step 3
Exam Tip
बाईं ओर जाने पर दूरी घटाई जाती है, इसलिए निर्देशांक \( -4-\sqrt{23} \) होगा। दिशा देखकर चिह्न चुनें।
\( \sqrt{21}\approx4.583 \), which is slightly less than (4.59). Use more accurate estimation for close values.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{21}<4.59 \). \( \sqrt{21}\approx4.583 \), which is slightly less than (4.59). Use more accurate estimation for close values.
Step 3
Exam Tip
\( \sqrt{21}\approx4.583 \), जो (4.59) से थोड़ा छोटा है। निकट मानों में अधिक सटीक अनुमान करें।
\( \sqrt{39}\approx6.245 \), so \(6-\sqrt{39}\approx-0.245\). Always check the sign in root subtraction.
Step 2
Why this answer is correct
The correct answer is A. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). \( \sqrt{39}\approx6.245 \), so \(6-\sqrt{39}\approx-0.245\). Always check the sign in root subtraction.
Step 3
Exam Tip
\( \sqrt{39}\approx6.245 \), इसलिए \(6-\sqrt{39}\approx-0.245\) है। घटाव वाले मूल में चिह्न जरूर जाँचें।
\( \sqrt{48}\approx6.928 \) and \( \sqrt{49}=7 \), so (6.95) lies between them. Use accurate estimation for close roots.
Step 2
Why this answer is correct
The correct answer is B. (6.95). \( \sqrt{48}\approx6.928 \) and \( \sqrt{49}=7 \), so (6.95) lies between them. Use accurate estimation for close roots.
Step 3
Exam Tip
\( \sqrt{48}\approx6.928 \) और \( \sqrt{49}=7 \), इसलिए (6.95) इनके बीच है। पास-पास मूलों में सटीक अनुमान करें।
The distance is ( \left|\frac{9}{10}-\left\(-\frac{17}{5}\right\)\right|=\frac{43}{10} ). Use absolute value while finding distance.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{43}{10} \). The distance is ( \left|\frac{9}{10}-\left\(-\frac{17}{5}\right\)\right|=\frac{43}{10} ). Use absolute value while finding distance.
Step 3
Exam Tip
दूरी ( \left|\frac{9}{10}-\left\(-\frac{17}{5}\right\)\right|=\frac{43}{10} ) है। दूरी निकालते समय निरपेक्ष मान लगाएँ।
\( \frac{41}{10}=4.1 \), \( \sqrt{17}\approx4.123 \), and (4.13). Convert close values to decimals for comparison.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{41}{10},\sqrt{17},4.13 \). \( \frac{41}{10}=4.1 \), \( \sqrt{17}\approx4.123 \), and (4.13). Convert close values to decimals for comparison.
Step 3
Exam Tip
\( \frac{41}{10}=4.1 \), \( \sqrt{17}\approx4.123 \), और (4.13) है। निकट मानों को दशमलव में बदलकर तुलना करें।
( |x-1.5|=4.25 ) means the distance of (x) from (1.5) is (4.25). Moving both directions gives ( -2.75 ) and (5.75).
Step 2
Why this answer is correct
The correct answer is A. ( -2.75 ) और (5.75) / ( -2.75 ) and (5.75). ( |x-1.5|=4.25 ) means the distance of (x) from (1.5) is (4.25). Moving both directions gives ( -2.75 ) and (5.75).
Step 3
Exam Tip
( |x-1.5|=4.25 ) का अर्थ (x) की (1.5) से दूरी (4.25) है। दोनों दिशाओं में ( -2.75 ) और (5.75) मिलते हैं।
\( \sqrt{126}\approx11.22 \) and \( \sqrt{80}\approx8.94 \), so the difference is about (2.28). Estimate both square roots first.
Step 2
Why this answer is correct
The correct answer is B. (2) और (3) / (2) and (3). \( \sqrt{126}\approx11.22 \) and \( \sqrt{80}\approx8.94 \), so the difference is about (2.28). Estimate both square roots first.
Step 3
Exam Tip
\( \sqrt{126}\approx11.22 \) और \( \sqrt{80}\approx8.94 \), इसलिए अंतर लगभग (2.28) है। पहले दोनों वर्गमूलों का अनुमान करें।
\( \sqrt{192}=8\sqrt{3} \) and \( \sqrt{75}=5\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{3}\). \( \sqrt{192}=8\sqrt{3} \) and \( \sqrt{75}=5\sqrt{3} \), so the difference is \(3\sqrt{3}\). Simplify the radicals first.
Step 3
Exam Tip
\( \sqrt{192}=8\sqrt{3} \) और \( \sqrt{75}=5\sqrt{3} \), इसलिए अंतर \(3\sqrt{3}\) है। पहले मूलों को सरल करें।
C. ( -7 ) और ( -6 ) के बीच/Between ( -7 ) and ( -6 )
Step 1
Concept
\( -\sqrt{18}-2\approx-6.243 \), so it lies between (-7) and (-6). Estimate negative sums carefully.
Step 2
Why this answer is correct
The correct answer is C. ( -7 ) और ( -6 ) के बीच / Between ( -7 ) and ( -6 ). \( -\sqrt{18}-2\approx-6.243 \), so it lies between (-7) and (-6). Estimate negative sums carefully.
Step 3
Exam Tip
\( -\sqrt{18}-2\approx-6.243 \), इसलिए यह (-7) और (-6) के बीच है। ऋणात्मक योगों में अनुमान सावधानी से करें।
Adding like radicals gives \( \sqrt{19}+\sqrt{19}+\sqrt{19}=3\sqrt{19} \). Do not add the numbers inside radicals directly.
Step 2
Why this answer is correct
The correct answer is B. \(3\sqrt{19}\). Adding like radicals gives \( \sqrt{19}+\sqrt{19}+\sqrt{19}=3\sqrt{19} \). Do not add the numbers inside radicals directly.
Step 3
Exam Tip
समान मूलों को जोड़ने पर \( \sqrt{19}+\sqrt{19}+\sqrt{19}=3\sqrt{19} \) होता है। मूल के अंदर संख्याएँ सीधे नहीं जोड़ी जातीं।
\( \sqrt{11}\approx3.317 \) and \( \sqrt{10}\approx3.162 \), so the difference is about (0.155). The difference of nearby roots is small.
Step 2
Why this answer is correct
The correct answer is B. (0.15). \( \sqrt{11}\approx3.317 \) and \( \sqrt{10}\approx3.162 \), so the difference is about (0.155). The difference of nearby roots is small.
Step 3
Exam Tip
\( \sqrt{11}\approx3.317 \) और \( \sqrt{10}\approx3.162 \), इसलिए अंतर लगभग (0.155) है। पास-पास मूलों का अंतर छोटा होता है।
\( -\frac{53}{20}=-2.65 \), \( -\sqrt{7}\approx-2.646 \), and (-2.64). For negative values, the smallest number comes first.
Step 2
Why this answer is correct
The correct answer is A. \( -\frac{53}{20},-\sqrt{7},-2.64 \). \( -\frac{53}{20}=-2.65 \), \( -\sqrt{7}\approx-2.646 \), and (-2.64). For negative values, the smallest number comes first.
Step 3
Exam Tip
\( -\frac{53}{20}=-2.65 \), \( -\sqrt{7}\approx-2.646 \), और (-2.64) है। ऋणात्मक मानों में सबसे छोटी संख्या पहले आती है।
\( \sqrt{2}\approx1.414 \), so \( \frac{a}{100} \) must be between (1.414) and (1.42). (a=141) gives (1.41), which is not correct.
Step 2
Why this answer is correct
The correct answer is A. (141). \( \sqrt{2}\approx1.414 \), so \( \frac{a}{100} \) must be between (1.414) and (1.42). (a=141) gives (1.41), which is not correct.
Step 3
Exam Tip
\( \sqrt{2}\approx1.414 \), इसलिए \( \frac{a}{100} \) को (1.414) और (1.42) के बीच होना चाहिए। (a=141) से (1.41) मिलता है जो सही नहीं है।
\(4-\sqrt{6}\approx1.551\) and \( \frac{31}{20}=1.55 \), so the first value is slightly greater. Estimate close values accurately.
Step 2
Why this answer is correct
The correct answer is B. \(4-\sqrt{6}>\frac{31}{20}\). \(4-\sqrt{6}\approx1.551\) and \( \frac{31}{20}=1.55 \), so the first value is slightly greater. Estimate close values accurately.
Step 3
Exam Tip
\(4-\sqrt{6}\approx1.551\) और \( \frac{31}{20}=1.55 \), इसलिए पहला मान थोड़ा बड़ा है। निकट मानों में सटीक अनुमान करें।
The point on the right is positive and its distance is \( \sqrt{26} \). Therefore the number is \( \sqrt{26} \).
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{26} \). The point on the right is positive and its distance is \( \sqrt{26} \). Therefore the number is \( \sqrt{26} \).
Step 3
Exam Tip
दाईं ओर का बिंदु धनात्मक होगा और दूरी \( \sqrt{26} \) है। इसलिए संख्या \( \sqrt{26} \) है।
\( \sqrt{8}+\frac{1}{10}\approx2.928 \). Therefore (2.90) does not satisfy it and no given value satisfies the condition.
Step 2
Why this answer is correct
The correct answer is A. (2.90). \( \sqrt{8}+\frac{1}{10}\approx2.928 \). Therefore (2.90) does not satisfy it and no given value satisfies the condition.
Step 3
Exam Tip
\( \sqrt{8}+\frac{1}{10}\approx2.928 \) है। इसलिए (2.90) नहीं बल्कि कोई भी दिया मान शर्त पूरी नहीं करता।
Moving \( \frac{7}{5} \) to the right of (-3) gives \( -3+\frac{7}{5}=-\frac{8}{5} \). Use the given interval to choose direction.
Step 2
Why this answer is correct
The correct answer is A. \( -\frac{8}{5} \). Moving \( \frac{7}{5} \) to the right of (-3) gives \( -3+\frac{7}{5}=-\frac{8}{5} \). Use the given interval to choose direction.
Step 3
Exam Tip
(-3) से दाईं ओर \( \frac{7}{5} \) जाने पर \( -3+\frac{7}{5}=-\frac{8}{5} \) मिलता है। दिए गए अंतराल से दिशा चुनें।
\(7.5^2=56.25\) and \(7.6^2=57.76\), so \( \sqrt{57} \) lies between them. Check squares for decimal bounds.
Step 2
Why this answer is correct
The correct answer is B. \(7.5<\sqrt{57}<7.6\). \(7.5^2=56.25\) and \(7.6^2=57.76\), so \( \sqrt{57} \) lies between them. Check squares for decimal bounds.
Step 3
Exam Tip
\(7.5^2=56.25\) और \(7.6^2=57.76\), इसलिए \( \sqrt{57} \) इनके बीच है। दशमलव सीमा के लिए वर्ग जाँचें।
Moving left gives \( \frac{9}{10}-\frac{7}{25}=\frac{31}{50} \). Subtract the distance according to direction.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{31}{50} \). Moving left gives \( \frac{9}{10}-\frac{7}{25}=\frac{31}{50} \). Subtract the distance according to direction.
Step 3
Exam Tip
बाईं ओर जाने पर \( \frac{9}{10}-\frac{7}{25}=\frac{31}{50} \) मिलता है। दिशा के अनुसार दूरी घटाएँ।
A. ( -6 ) और ( -5 ) के बीच/Between ( -6 ) and ( -5 )
Step 1
Concept
\( \sqrt{68}\approx8.246 \), so \(p\approx-5.246\). Hence it lies between (-6) and (-5).
Step 2
Why this answer is correct
The correct answer is A. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 ). \( \sqrt{68}\approx8.246 \), so \(p\approx-5.246\). Hence it lies between (-6) and (-5).
Step 3
Exam Tip
\( \sqrt{68}\approx8.246 \), इसलिए \(p\approx-5.246\) है। इसलिए यह (-6) और (-5) के बीच है।
