Choose the correct relation: (i) \(\sqrt{10} < 3.2\) (ii) \(\sqrt{11} < \sqrt{12}\) (iii) \(\sqrt{13} < \sqrt{14}\)
(i), (ii) and (iii)
Check each relation independently.
(i) Compare \(\sqrt{10}\) with \(3.2\) by squaring both sides (both positive):
\((\sqrt{10})^2 = 10,\quad (3.2)^2 = 10.24\)
Since \(10 < 10.24\), we have \(\sqrt{10} < 3.2\). True.
(ii) & (iii) The square-root function is strictly increasing for non-negative numbers. So \(11 < 12\) gives \(\sqrt{11} < \sqrt{12}\), and \(13 < 14\) gives \(\sqrt{13} < \sqrt{14}\). Both true.
Hence all three relations are correct — option (4).
Similar Questions
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Rationalize:
$\frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}$- Simplify:
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$\frac{\sqrt{5+2\sqrt{6}} + \sqrt{5-2\sqrt{6}}}{\sqrt{2}}$
Important Questions from Surds and Indices
The value of \(\frac{{{{\left( {251} \right)}^3} + {{\left( {249} \right)}^3}}}{{25.1 \times 25.1 - 624.99 + 24.9 \times 24.9}}\) is 5 × 10 k , where the value of k is :
Find the value of m in \(\left(\frac{2}{7}\right)^{-3} \times \left(\frac{2}{7}\right)^{-5}=\left (\frac{2}{7}\right)^{-3m+1}\)
If √625 = 25; then√(.00000625/25)is:
A. 0.0025
B. 0.001
C. 0.0001
D. 0.0005Find the value of:
\(\sqrt{150}-\sqrt{54}-\sqrt{24}\)
If \(\sqrt{4624}=68\) , then the value of:
\(\sqrt{46.24}+\sqrt{0.4624}+\sqrt{0.004624}\)
