\( -\frac{43}{11}\approx-3.909 \), 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।
