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।
\( -\frac{43}{11}\approx-3.909 \), 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।
\( \sqrt{39}\approx6.245 \), 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।
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।
\( -\frac{31}{9}\approx-3.444 \), 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।
\( \sqrt{31}\approx5.568 \), 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।
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।
\( \sqrt{18}\approx4.243 \), 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 \(4<\sqrt{22}<5\), \(-1<-5+\sqrt{22}<0\). 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।
C. यह (-4) और (-3) के बीच है/It lies between (-4) and (-3)
Step 1
Concept
\( -\frac{19}{6}\approx-3.167 \), so it lies between (-4) and (-3). Converting a negative fraction to decimal is useful.
Step 2
Why this answer is correct
The correct answer is C. यह (-4) और (-3) के बीच है / It lies between (-4) and (-3). \( -\frac{19}{6}\approx-3.167 \), so it lies between (-4) and (-3). Converting a negative fraction to decimal is useful.
Step 3
Exam Tip
\( -\frac{19}{6}\approx-3.167 \), इसलिए यह (-4) और (-3) के बीच है। ऋणात्मक भिन्न को दशमलव में बदलना उपयोगी है।
B. ( -6 ) और ( -5 ) के बीच/Between ( -6 ) and ( -5 )
Step 1
Concept
Since \(5<\sqrt{29}<6\), \(-6<-\sqrt{29}<-5\). For negative roots, write the reversed interval carefully.
Step 2
Why this answer is correct
The correct answer is B. ( -6 ) और ( -5 ) के बीच / Between ( -6 ) and ( -5 ). Since \(5<\sqrt{29}<6\), \(-6<-\sqrt{29}<-5\). For negative roots, write the reversed interval carefully.
Step 3
Exam Tip
क्योंकि \(5<\sqrt{29}<6\), इसलिए \(-6<-\sqrt{29}<-5\)। ऋणात्मक मूलों में क्रम उलटकर लिखें।
A. ( -3 ) और ( -2 ) के बीच/Between ( -3 ) and ( -2 )
Step 1
Concept
\( -\sqrt{2}-1\approx-2.414 \), so it lies between (-3) and (-2). Estimate negative sums carefully.
Step 2
Why this answer is correct
The correct answer is A. ( -3 ) और ( -2 ) के बीच / Between ( -3 ) and ( -2 ). \( -\sqrt{2}-1\approx-2.414 \), so it lies between (-3) and (-2). Estimate negative sums carefully.
Step 3
Exam Tip
\( -\sqrt{2}-1\approx-2.414 \), इसलिए यह (-3) और (-2) के बीच है। ऋणात्मक योगों में अनुमान सावधानी से करें।
\( \sqrt{10}\approx3.162 \), so \(2-\sqrt{10}\approx-1.162\). Estimation is important in root subtraction.
Step 2
Why this answer is correct
The correct answer is A. (-2) और (-1) के बीच / Between (-2) and (-1). \( \sqrt{10}\approx3.162 \), so \(2-\sqrt{10}\approx-1.162\). Estimation is important in root subtraction.
Step 3
Exam Tip
\( \sqrt{10}\approx3.162 \) इसलिए \(2-\sqrt{10}\approx-1.162\) है। घटाव वाले मूल में अनुमान जरूरी है।
\( \sqrt{5}\approx2.236\), so \(2-\sqrt{5}\approx-0.236\). Estimation is fastest for subtraction with roots.
Step 2
Why this answer is correct
The correct answer is A. (-1) और (0) के बीच / Between (-1) and (0). \( \sqrt{5}\approx2.236\), so \(2-\sqrt{5}\approx-0.236\). Estimation is fastest for subtraction with roots.
Step 3
Exam Tip
\( \sqrt{5}\approx2.236\), इसलिए \(2-\sqrt{5}\approx-0.236\)। घटाव वाले मूलों में अनुमान सबसे तेज होता है।
Since \(6<\sqrt{48}<7\), \(-7<-\sqrt{48}<-6\). Write the interval carefully for negative square roots.
Step 2
Why this answer is correct
The correct answer is A. (-7) और (-6) / (-7) and (-6). Since \(6<\sqrt{48}<7\), \(-7<-\sqrt{48}<-6\). Write the interval carefully for negative square roots.
Step 3
Exam Tip
\(6<\sqrt{48}<7\), इसलिए \(-7<-\sqrt{48}<-6\)। ऋणात्मक वर्गमूल में अंतराल उल्टा लिखें।
\(x=-4+\sqrt{13}\), and \(3<\sqrt{13}<4\), so (-1<x<0). Add bounds in combined expressions.
Step 2
Why this answer is correct
The correct answer is A. (-1) और (0) के बीच / Between (-1) and (0). \(x=-4+\sqrt{13}\), and \(3<\sqrt{13}<4\), so (-1<x<0). Add bounds in combined expressions.
Step 3
Exam Tip
\(x=-4+\sqrt{13}\) और \(3<\sqrt{13}<4\), इसलिए (-1<x<0)। संयुक्त अभिव्यक्ति में सीमा जोड़ें।
\(\sqrt{5}\approx2.236\) and \(\sqrt{2}\approx1.414\), so the difference is about (0.822). Use short approximations to locate differences of irrationals.
Step 2
Why this answer is correct
The correct answer is A. ((0,1)). \(\sqrt{5}\approx2.236\) and \(\sqrt{2}\approx1.414\), so the difference is about (0.822). Use short approximations to locate differences of irrationals.
Step 3
Exam Tip
\(\sqrt{5}\approx2.236\) और \(\sqrt{2}\approx1.414\), इसलिए अंतर लगभग (0.822) है। अपरिमेयों के अंतर का स्थान निकालने के लिए छोटे अनुमान उपयोग करें।
Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3), so \(-\sqrt{5}\) lies between (-3) and (-2). On the negative side, order reverses.
Step 2
Why this answer is correct
The correct answer is A. ((-3,-2)). Since \(2^2<5<3^2\), \(\sqrt{5}\) lies between (2) and (3), so \(-\sqrt{5}\) lies between (-3) and (-2). On the negative side, order reverses.
Step 3
Exam Tip
क्योंकि \(2^2<5<3^2\), इसलिए \(\sqrt{5}\) (2) और (3) के बीच है और ऋणात्मक मान (-3) और (-2) के बीच होगा। ऋणात्मक दिशा में क्रम उलट जाता है।
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.
Step 2
Why this answer is correct
The correct answer is A. (0) और (1) / (0) and (1). 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.
Step 3
Exam Tip
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।
\(\sqrt{11}\) lies between (3) and (4), so \(-\sqrt{11}\) lies between (-4) and (-3). The negative sign changes the side.
Step 2
Why this answer is correct
The correct answer is C. (-4) और (-3) / (-4) and (-3). \(\sqrt{11}\) lies between (3) and (4), so \(-\sqrt{11}\) lies between (-4) and (-3). The negative sign changes the side.
Step 3
Exam Tip
\(\sqrt{11}\) (3) और (4) के बीच है इसलिए \(-\sqrt{11}\) (-4) और (-3) के बीच होगा। ऋणात्मक चिन्ह दिशा बदल देता है।
Since \(7^2<50<8^2\), \(\sqrt{50}\) lies between (7) and (8). Use perfect squares to decide the interval.
Step 2
Why this answer is correct
The correct answer is C. (7) और (8) / (7) and (8). Since \(7^2<50<8^2\), \(\sqrt{50}\) lies between (7) and (8). Use perfect squares to decide the interval.
Step 3
Exam Tip
क्योंकि \(7^2<50<8^2\), इसलिए \(\sqrt{50}\) (7) और (8) के बीच है। पूर्ण वर्गों से अंतराल तय करें।
A. यह (-2) और (-3) के बीच है/It is between (-2) and (-3)
Step 1
Concept
\(\frac{-13}{6}\approx -2.17\), so it lies between (-3) and (-2). Intervals with negative numbers can be tricky.
Step 2
Why this answer is correct
The correct answer is A. यह (-2) और (-3) के बीच है / It is between (-2) and (-3). \(\frac{-13}{6}\approx -2.17\), so it lies between (-3) and (-2). Intervals with negative numbers can be tricky.
Step 3
Exam Tip
\(\frac{-13}{6}\approx -2.17\), इसलिए यह (-3) और (-2) के बीच है। ऋणात्मक संख्या में पूर्णांक अंतराल उलझा सकता है।
