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।
