\( \sqrt{91}\approx9.54 \) and \( \sqrt{55}\approx7.42 \), so the difference is about (2.12). Estimate both roots first.
Step 2
Why this answer is correct
The correct answer is B. (2) और (3) / (2) and (3). \( \sqrt{91}\approx9.54 \) and \( \sqrt{55}\approx7.42 \), so the difference is about (2.12). Estimate both roots first.
Step 3
Exam Tip
\( \sqrt{91}\approx9.54 \) और \( \sqrt{55}\approx7.42 \), इसलिए अंतर लगभग (2.12) है। पहले दोनों मूलों का अनुमान करें।
( |x+2.5|=3.75 ) means the distance of (x) from (-2.5) is (3.75). Moving both ways gives (1.25) and (-6.25).
Step 2
Why this answer is correct
The correct answer is A. (1.25) और (-6.25) / (1.25) and (-6.25). ( |x+2.5|=3.75 ) means the distance of (x) from (-2.5) is (3.75). Moving both ways gives (1.25) and (-6.25).
Step 3
Exam Tip
( |x+2.5|=3.75 ) का अर्थ (x) की (-2.5) से दूरी (3.75) है। दोनों दिशाओं में (1.25) और (-6.25) मिलते हैं।
\( \sqrt{13}\approx3.606 \), (3.61), and \( \frac{29}{8}=3.625 \). Compare close values to more decimal places.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{13},3.61,\frac{29}{8} \). \( \sqrt{13}\approx3.606 \), (3.61), and \( \frac{29}{8}=3.625 \). Compare close values to more decimal places.
Step 3
Exam Tip
\( \sqrt{13}\approx3.606 \), (3.61) और \( \frac{29}{8}=3.625 \) है। निकट मानों में अधिक दशमलव स्थान तक तुलना करें।
The distance is ( \left|\frac{7}{6}-\left\(-\frac{11}{4}\right\)\right|=\frac{47}{12} ). Use absolute value while finding distance.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{47}{12} \). The distance is ( \left|\frac{7}{6}-\left\(-\frac{11}{4}\right\)\right|=\frac{47}{12} ). Use absolute value while finding distance.
Step 3
Exam Tip
दूरी ( \left|\frac{7}{6}-\left\(-\frac{11}{4}\right\)\right|=\frac{47}{12} ) है। दूरी निकालते समय निरपेक्ष मान लगाएँ।
\( \sqrt{33}\approx5.745 \) and \( \sqrt{34}\approx5.831 \), so (5.75) lies between them. Keep estimates accurate for close roots.
Step 2
Why this answer is correct
The correct answer is B. (5.75). \( \sqrt{33}\approx5.745 \) and \( \sqrt{34}\approx5.831 \), so (5.75) lies between them. Keep estimates accurate for close roots.
Step 3
Exam Tip
\( \sqrt{33}\approx5.745 \) और \( \sqrt{34}\approx5.831 \), इसलिए (5.75) इनके बीच है। निकट वर्गमूलों में अनुमान सटीक रखें।
\( \sqrt{31}\approx5.568 \), so \(5-\sqrt{31}\approx-0.568\). Always check the sign in root subtraction.
Step 2
Why this answer is correct
The correct answer is B. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). \( \sqrt{31}\approx5.568 \), so \(5-\sqrt{31}\approx-0.568\). Always check the sign in root subtraction.
Step 3
Exam Tip
\( \sqrt{31}\approx5.568 \), इसलिए \(5-\sqrt{31}\approx-0.568\) है। घटाव वाले मूलों में चिह्न अवश्य जाँचें।
\( \sqrt{15}\approx3.873 \), which is slightly less than (3.88). Use more accurate estimation for close values.
Step 2
Why this answer is correct
The correct answer is B. \( \sqrt{15}<3.88 \). \( \sqrt{15}\approx3.873 \), which is slightly less than (3.88). Use more accurate estimation for close values.
Step 3
Exam Tip
\( \sqrt{15}\approx3.873 \), जो (3.88) से थोड़ा छोटा है। निकट मानों में अधिक सटीक अनुमान करें।
Moving left means subtracting the distance, so the coordinate is \(2-\sqrt{19}\). Choose the sign by direction.
Step 2
Why this answer is correct
The correct answer is C. \(2-\sqrt{19}\). Moving left means subtracting the distance, so the coordinate is \(2-\sqrt{19}\). Choose the sign by direction.
Step 3
Exam Tip
बाईं ओर जाने पर दूरी घटाई जाती है, इसलिए निर्देशांक \(2-\sqrt{19}\) है। दिशा देखकर चिह्न चुनें।
\( -\sqrt{10}\approx-3.162 \) and \( -\frac{19}{6}\approx-3.167 \). (-3.20) is not between them, so recheck direction for close negative values.
Step 2
Why this answer is correct
The correct answer is A. ( -3.20 ). \( -\sqrt{10}\approx-3.162 \) and \( -\frac{19}{6}\approx-3.167 \). (-3.20) is not between them, so recheck direction for close negative values.
Step 3
Exam Tip
\( -\sqrt{10}\approx-3.162 \) और \( -\frac{19}{6}\approx-3.167 \) है। (-3.20) इनके बीच नहीं है, इसलिए निकट ऋणात्मक मानों में दिशा दोबारा जाँचें।
\( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
Step 2
Why this answer is correct
The correct answer is A. \(2\sqrt{3}\). \( \sqrt{75}=5\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the difference is \(2\sqrt{3}\). Subtract only like radicals.
Step 3
Exam Tip
\( \sqrt{75}=5\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए अंतर \(2\sqrt{3}\) है। समान मूलों को ही घटाएँ।
This decimal is non-terminating and non-repeating, so it is irrational. Check carefully whether the pattern 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 carefully whether the pattern repeats or not.
Step 3
Exam Tip
यह दशमलव असांत और अनावर्ती है, इसलिए अपरिमेय है। पैटर्न दोहराव वाला है या नहीं, इसे ध्यान से देखें।
\( -\frac{31}{9}\approx-3.444 \), 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 ). \( -\frac{31}{9}\approx-3.444 \), so it lies between (-4) and (-3). Convert negative fractions to decimals.
Step 3
Exam Tip
\( -\frac{31}{9}\approx-3.444 \), इसलिए यह (-4) और (-3) के बीच है। ऋणात्मक भिन्नों को दशमलव में बदलें।
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।
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।
\(7.5^2=56.25\) 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 \( \frac{7}{5} \) 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।
\( \sqrt{8}+\frac{1}{10}\approx2.928 \). 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।
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।
\(4-\sqrt{6}\approx1.551\) 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।
\( \sqrt{2}\approx1.414 \), 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।
\( -\frac{53}{20}=-2.65 \), \( -\sqrt{7}\approx-2.646 \), 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।
\( \sqrt{11}\approx3.317 \) 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।
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।
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।
\( \sqrt{192}=8\sqrt{3} \) 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।
