\( \sqrt{31}\approx5.568 \), 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।
\( \sqrt{33}\approx5.745 \) 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।
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।
\( \sqrt{13}\approx3.606 \), (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।
( |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।
\( \sqrt{91}\approx9.54 \) 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।
\( \sqrt{6}\approx2.449 \) and \( \frac{1}{3}\approx0.333 \), so the sum is about (2.782). For mixed values, estimate first.
Step 2
Why this answer is correct
The correct answer is B. (2) और (3) / (2) and (3). \( \sqrt{6}\approx2.449 \) and \( \frac{1}{3}\approx0.333 \), so the sum is about (2.782). For mixed values, estimate first.
Step 3
Exam Tip
\( \sqrt{6}\approx2.449 \) और \( \frac{1}{3}\approx0.333 \), इसलिए योग लगभग (2.782) है। मिश्रित मानों में पहले अनुमान लगाएँ।
C. ( -5 ) और ( -4 ) के बीच/Between ( -5 ) and ( -4 )
Step 1
Concept
\( \sqrt{7}\approx2.646 \), so \(u\approx-4.646\). Therefore it lies between (-5) and (-4).
Step 2
Why this answer is correct
The correct answer is C. ( -5 ) और ( -4 ) के बीच / Between ( -5 ) and ( -4 ). \( \sqrt{7}\approx2.646 \), so \(u\approx-4.646\). Therefore it lies between (-5) and (-4).
Step 3
Exam Tip
\( \sqrt{7}\approx2.646 \), इसलिए \(u\approx-4.646\) है। अतः यह (-5) और (-4) के बीच होगा।
\( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the sum is \(5\sqrt{3}\). Simplify the radicals first.
Step 2
Why this answer is correct
The correct answer is B. \(5\sqrt{3}\). \( \sqrt{12}=2\sqrt{3} \) and \( \sqrt{27}=3\sqrt{3} \), so the sum is \(5\sqrt{3}\). Simplify the radicals first.
Step 3
Exam Tip
\( \sqrt{12}=2\sqrt{3} \) और \( \sqrt{27}=3\sqrt{3} \), इसलिए योग \(5\sqrt{3}\) है। पहले मूलों को सरल करें।
\( -\sqrt{13}\approx-3.606 \), so (-3.65) is less than it and greater than (-3.7). Be careful with direction for negative values.
Step 2
Why this answer is correct
The correct answer is C. ( -3.65 ). \( -\sqrt{13}\approx-3.606 \), so (-3.65) is less than it and greater than (-3.7). Be careful with direction for negative values.
Step 3
Exam Tip
\( -\sqrt{13}\approx-3.606 \), इसलिए (-3.65) इससे छोटा और (-3.7) से बड़ा है। ऋणात्मक मानों में दिशा सावधानी से देखें।
\( \frac{13}{3}\approx4.333 \), \( \sqrt{19}\approx4.359 \), and (4.34) lies between them. The correct order is \( \frac{13}{3},4.34,\sqrt{19} \).
Step 2
Why this answer is correct
The correct answer is D. \( \frac{13}{3},\sqrt{19},4.34 \). \( \frac{13}{3}\approx4.333 \), \( \sqrt{19}\approx4.359 \), and (4.34) lies between them. The correct order is \( \frac{13}{3},4.34,\sqrt{19} \).
Step 3
Exam Tip
\( \frac{13}{3}\approx4.333 \), \( \sqrt{19}\approx4.359 \), और (4.34) इनके बीच है। सही क्रम \( \frac{13}{3},4.34,\sqrt{19} \) है।
\( \sqrt{11}\approx3.316 \) and \( \frac{10}{3}\approx3.333 \), so (3.33) lies between them. Compare very close values accurately.
Step 2
Why this answer is correct
The correct answer is C. (3.33). \( \sqrt{11}\approx3.316 \) and \( \frac{10}{3}\approx3.333 \), so (3.33) lies between them. Compare very close values accurately.
Step 3
Exam Tip
\( \sqrt{11}\approx3.316 \) और \( \frac{10}{3}\approx3.333 \), इसलिए (3.33) बीच में है। बहुत पास मानों में सटीक तुलना करें।
\( \sqrt{\frac{81}{196}}=\frac{9}{14} \). Take the positive square root of both numerator and denominator.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{9}{14} \). \( \sqrt{\frac{81}{196}}=\frac{9}{14} \). Take the positive square root of both numerator and denominator.
Step 3
Exam Tip
\( \sqrt{\frac{81}{196}}=\frac{9}{14} \) है। अंश और हर दोनों का धनात्मक वर्गमूल लें।
\( \sqrt{18}\approx4.243 \), so \(4-\sqrt{18}\approx-0.243\). The sign can change when subtracting a root.
Step 2
Why this answer is correct
The correct answer is A. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). \( \sqrt{18}\approx4.243 \), so \(4-\sqrt{18}\approx-0.243\). The sign can change when subtracting a root.
Step 3
Exam Tip
\( \sqrt{18}\approx4.243 \), इसलिए \(4-\sqrt{18}\approx-0.243\)। मूल घटाने पर चिह्न बदल सकता है।
Since \(8<\sqrt{80}<9\), \(-9<-\sqrt{80}<-8\). Write intervals carefully for negative roots.
Step 2
Why this answer is correct
The correct answer is A. ( -9 ) और ( -8 ) / ( -9 ) and ( -8 ). Since \(8<\sqrt{80}<9\), \(-9<-\sqrt{80}<-8\). Write intervals carefully for negative roots.
Step 3
Exam Tip
क्योंकि \(8<\sqrt{80}<9\), इसलिए \(-9<-\sqrt{80}<-8\)। ऋणात्मक मूलों में अंतराल सावधानी से लिखें।
\( \sqrt{3}\approx1.732 \), \( \frac{7}{4}=1.75 \), and (1.76) are in this increasing order. Compare all values as decimals.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{3},\frac{7}{4},1.76 \). \( \sqrt{3}\approx1.732 \), \( \frac{7}{4}=1.75 \), and (1.76) are in this increasing order. Compare all values as decimals.
Step 3
Exam Tip
\( \sqrt{3}\approx1.732 \), \( \frac{7}{4}=1.75 \), और (1.76) है। इसलिए यही बढ़ता क्रम है।
Moving right gives \( -\frac{5}{4}+\frac{7}{10}=-\frac{11}{20} \). Use a common denominator to add fractions.
Step 2
Why this answer is correct
The correct answer is A. \( -\frac{11}{20} \). Moving right gives \( -\frac{5}{4}+\frac{7}{10}=-\frac{11}{20} \). Use a common denominator to add fractions.
Step 3
Exam Tip
दाईं ओर \( -\frac{5}{4}+\frac{7}{10}=-\frac{11}{20} \) मिलता है। भिन्नों में समान हर बनाकर जोड़ें।
Since \(4<\sqrt{22}<5\), \(-1<-5+\sqrt{22}<0\). Add bounds carefully in mixed expressions.
Step 2
Why this answer is correct
The correct answer is C. ( -1 ) और (0) के बीच / Between ( -1 ) and (0). Since \(4<\sqrt{22}<5\), \(-1<-5+\sqrt{22}<0\). Add bounds carefully in mixed expressions.
Step 3
Exam Tip
\(4<\sqrt{22}<5\), इसलिए \(-1<-5+\sqrt{22}<0\)। मिश्रित अभिव्यक्ति में सीमा जोड़ें।
