\( \sqrt{5}\approx2.236\), 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।
\( \frac{5}{3}\approx1.667\), (1.7=1.7), and \( \sqrt{3}\approx1.732\). Convert mixed forms to decimals for ordering.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{5}{3},1.7,\sqrt{3}\). \( \frac{5}{3}\approx1.667\), (1.7=1.7), and \( \sqrt{3}\approx1.732\). Convert mixed forms to decimals for ordering.
Step 3
Exam Tip
\( \frac{5}{3}\approx1.667\), (1.7=1.7), और \( \sqrt{3}\approx1.732\)। मिश्रित संख्याओं को दशमलव में बदलकर क्रम लगाएँ।
\(x=-4+\sqrt{13}\), 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।
\(3.8^2=14.44\) and \(3.9^2=15.21\), so \( \sqrt{15}\) lies between them. Check squares for decimal bounds.
Step 2
Why this answer is correct
The correct answer is A. (3.8) और (3.9) के बीच / Between (3.8) and (3.9). \(3.8^2=14.44\) and \(3.9^2=15.21\), so \( \sqrt{15}\) lies between them. Check squares for decimal bounds.
Step 3
Exam Tip
\(3.8^2=14.44\) और \(3.9^2=15.21\), इसलिए \( \sqrt{15}\) इनके बीच है। दशमलव सीमा के लिए वर्ग जाँचें।
\( \frac{22}{7}\approx3.142857\) and \( \pi\approx3.14159\), so \( \frac{22}{7}\) is slightly larger. Do not treat common approximations as exactly equal.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{22}{7}>\pi\). \( \frac{22}{7}\approx3.142857\) and \( \pi\approx3.14159\), so \( \frac{22}{7}\) is slightly larger. Do not treat common approximations as exactly equal.
Step 3
Exam Tip
\( \frac{22}{7}\approx3.142857\) और \( \pi\approx3.14159\), इसलिए \( \frac{22}{7}\) थोड़ा बड़ा है। प्रसिद्ध अनुमानों को बराबर न मानें।
The midpoint is \( \frac{-\frac{9}{2}-\frac{1}{2}}{2}=-\frac{5}{2}\). Add the fractions first, then divide by (2).
Step 2
Why this answer is correct
The correct answer is A. \( -\frac{5}{2}\). The midpoint is \( \frac{-\frac{9}{2}-\frac{1}{2}}{2}=-\frac{5}{2}\). Add the fractions first, then divide by (2).
Step 3
Exam Tip
मध्य बिंदु \( \frac{-\frac{9}{2}-\frac{1}{2}}{2}=-\frac{5}{2}\) है। भिन्नों में पहले योग करें, फिर (2) से भाग दें।
\( \sqrt{3}\approx1.732\) and \( \frac{7}{4}=1.75\), so \( \sqrt{3}\) is slightly smaller. Use decimal comparison for close values.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{3}<\frac{7}{4}\). \( \sqrt{3}\approx1.732\) and \( \frac{7}{4}=1.75\), so \( \sqrt{3}\) is slightly smaller. Use decimal comparison for close values.
Step 3
Exam Tip
\( \sqrt{3}\approx1.732\) और \( \frac{7}{4}=1.75\), इसलिए \( \sqrt{3}\) थोड़ा छोटा है। निकट मानों में दशमलव तुलना करें।
\(0.4040040004\ldots\) is non-terminating and non-repeating, so it is irrational. Observe the decimal pattern carefully.
Step 2
Why this answer is correct
The correct answer is A. अपरिमेय संख्या / Irrational number. \(0.4040040004\ldots\) is non-terminating and non-repeating, so it is irrational. Observe the decimal pattern carefully.
Step 3
Exam Tip
\(0.4040040004\ldots\) अनावर्ती और असांत दशमलव है, इसलिए यह अपरिमेय है। दशमलव के पैटर्न को ध्यान से देखें।
With perpendicular sides (1) and (1), the hypotenuse is \( \sqrt{2}\). Understand the construction using Pythagoras theorem.
Step 2
Why this answer is correct
The correct answer is A. \( \sqrt{1^2+1^2}\). With perpendicular sides (1) and (1), the hypotenuse is \( \sqrt{2}\). Understand the construction using Pythagoras theorem.
Step 3
Exam Tip
समकोण त्रिभुज में भुजाएँ (1) और (1) लेने पर कर्ण \( \sqrt{2}\) होता है। पायथागोरस प्रमेय से निर्माण समझें।
Both (1.999) and (2.001) are at distance (0.001) from (2). Points at equal distance are equally close.
Step 2
Why this answer is correct
The correct answer is A. (1.999) और (2.001) / (1.999) and (2.001). Both (1.999) and (2.001) are at distance (0.001) from (2). Points at equal distance are equally close.
Step 3
Exam Tip
(1.999) और (2.001) दोनों की (2) से दूरी (0.001) है। समान दूरी वाले दोनों बिंदु समान रूप से निकट होते हैं।
\( \sqrt{11}\approx3.316\), so \(p\approx-3.316\), which is less than (-3). Be careful with direction while comparing negatives.
Step 2
Why this answer is correct
The correct answer is A. (p<q). \( \sqrt{11}\approx3.316\), so \(p\approx-3.316\), which is less than (-3). Be careful with direction while comparing negatives.
Step 3
Exam Tip
\( \sqrt{11}\approx3.316\), इसलिए \(p\approx-3.316\) और यह (-3) से छोटा है। ऋणात्मक संख्याओं की तुलना में दिशा का ध्यान रखें।
\( \frac{3}{7}\approx0.428\), \( \frac{1}{2}=0.5\), and \( \frac{4}{7}\approx0.571\). Use decimals or cross multiplication to compare fractions.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{1}{2}\). \( \frac{3}{7}\approx0.428\), \( \frac{1}{2}=0.5\), and \( \frac{4}{7}\approx0.571\). Use decimals or cross multiplication to compare fractions.
Step 3
Exam Tip
\( \frac{3}{7}\approx0.428\), \( \frac{1}{2}=0.5\), और \( \frac{4}{7}\approx0.571\)। भिन्नों की तुलना में दशमलव या क्रॉस गुणन उपयोग करें।
\( \sqrt{20}\approx4.47\) and \( \sqrt{27}\approx5.19\), so (5) lies between them. Use perfect squares to identify bounds.
Step 2
Why this answer is correct
The correct answer is A. (5). \( \sqrt{20}\approx4.47\) and \( \sqrt{27}\approx5.19\), so (5) lies between them. Use perfect squares to identify bounds.
Step 3
Exam Tip
\( \sqrt{20}\approx4.47\) और \( \sqrt{27}\approx5.19\), इसलिए (5) बीच में है। पूर्ण वर्गों से सीमा पहचानें।
The distance from \( -\frac{5}{6}\) to (-1) is \( \frac{1}{6}\), and to (0) is \( \frac{5}{6}\). Closeness depends on the smaller distance.
Step 2
Why this answer is correct
The correct answer is A. ( -1). The distance from \( -\frac{5}{6}\) to (-1) is \( \frac{1}{6}\), and to (0) is \( \frac{5}{6}\). Closeness depends on the smaller distance.
Step 3
Exam Tip
\( -\frac{5}{6}\) की (-1) से दूरी \( \frac{1}{6}\) और (0) से दूरी \( \frac{5}{6}\) है। छोटी दूरी से निकटता तय होती है।
A. यह (3) और (4) के बीच है/It lies between (3) and (4)
Step 1
Concept
\( \sqrt{2}\approx1.414\) and \( \sqrt{3}\approx1.732\), so the sum is about (3.146). Estimation is a safe method for such sums.
Step 2
Why this answer is correct
The correct answer is A. यह (3) और (4) के बीच है / It lies between (3) and (4). \( \sqrt{2}\approx1.414\) and \( \sqrt{3}\approx1.732\), so the sum is about (3.146). Estimation is a safe method for such sums.
Step 3
Exam Tip
\( \sqrt{2}\approx1.414\) और \( \sqrt{3}\approx1.732\), योग लगभग (3.146) है। कठिन योगों में अनुमान लगाना सुरक्षित तरीका है।
( |x-2|=3) means the distance of (x) from (2) is (3), so (x=-1) or (x=5). Check both directions in distance questions.
Step 2
Why this answer is correct
The correct answer is A. ( -1) और (5) / ( -1) and (5). ( |x-2|=3) means the distance of (x) from (2) is (3), so (x=-1) or (x=5). Check both directions in distance questions.
Step 3
Exam Tip
( |x-2|=3) का अर्थ (x) की (2) से दूरी (3) है, इसलिए (x=-1) या (x=5)। दूरी वाले प्रश्न में दोनों दिशाएँ जाँचें।
A. यह (0) से (1) तक के आठ बराबर भागों में सातवें भाग पर है/It is at the seventh of eight equal parts from (0) to (1)
Step 1
Concept
\( \frac{7}{8}\) means (7) parts out of (8) equal parts from (0) to (1). The denominator gives the number of equal parts.
Step 2
Why this answer is correct
The correct answer is A. यह (0) से (1) तक के आठ बराबर भागों में सातवें भाग पर है / It is at the seventh of eight equal parts from (0) to (1). \( \frac{7}{8}\) means (7) parts out of (8) equal parts from (0) to (1). The denominator gives the number of equal parts.
Step 3
Exam Tip
\( \frac{7}{8}\) का अर्थ (0) से (1) तक (8) बराबर भागों में (7) भाग है। हर बराबर भागों की संख्या बताता है।
