Free Practice Questions for Square-and-square-root in Maths

$\begin{aligned} \sqrt{\frac{8}{3}} &=\sqrt{\frac{8 \times 3}{3 \times 3}} \\ &=\frac{\sqrt{24}}{3}=\frac{4.898}{3}=1.633 \text { लगभग } \end{aligned}$

$
\begin{aligned}
&\frac{2707}{\sqrt{x}}=27.07 \\
&\Rightarrow \sqrt{x}=\frac{2707}{27.07}=\frac{2707 \times 100}{2707}=100
\end{aligned}
$
दोनों ओर का वर्ग करने पर,
$
x=(100)^{2}=10000
$

पाँच अंकों की बड़ी से बड़ी संख्या $=99999$

अतः अभीष्ट संख्या $=99999-143$
$=99856$

$\begin{aligned} \frac{\sqrt{24}+\sqrt{216}}{\sqrt{96}} &=\frac{\sqrt{6 \times 4}+\sqrt{6 \times 6 \times 6}}{\sqrt{16 \times 6}} \\ &=\frac{2 \sqrt{6}+6 \sqrt{6}}{4 \sqrt{6}}=\frac{8 \sqrt{6}}{4 \sqrt{6}}=2 \end{aligned}$

$\sqrt{75.24+x}=8.71$
$\Rightarrow \quad 75.24+x=75.8641$
$\Rightarrow \quad x=75.8641-75.24$
$\Rightarrow \quad x=0.6241$

$\begin{aligned} \sqrt{\frac{0.081 \times 0.484}{0.0064 \times 6.25}} \\ &=\sqrt{\frac{81 \times 484}{64 \times 625}} \\ &=\frac{9 \times 22}{8 \times 25} \\ &=\frac{198}{200}=0.99 \end{aligned}$

$\begin{aligned} \sqrt{\frac{0.289}{0.00121}} &=\sqrt{\frac{289 \times 100}{121}} \\ &=\frac{17 \times 10}{11} \\ &=\frac{170}{11} \end{aligned}$

$\frac{\sqrt{32.4}}{\sqrt{x}}=2$
$\Rightarrow \quad \frac{32.4}{x}=4$
$\Rightarrow \quad x=\frac{32.4}{4}=8.1$

$\frac{x}{\sqrt{0.09}}=12$
$\Rightarrow \frac{x}{0.3}=12$
$\Rightarrow \quad x=3.6$

$\sqrt{1+\frac{25}{144}}=1+\frac{x}{12}$
$\Rightarrow \sqrt{\frac{144+25}{144}}=1+\frac{x}{12}$
$\Rightarrow \quad \sqrt{\frac{169}{144}}=1+\frac{x}{12}$
$\Rightarrow \quad \frac{13}{12}-1=\frac{x}{12}$
$\Rightarrow \quad \frac{13-12}{12}=\frac{x}{12}$
$\Rightarrow \quad x=1$

$\sqrt{15612+\sqrt{154+\sqrt{225}}}$
$=\sqrt{15612+\sqrt{154+15}}$
$=\sqrt{15612+\sqrt{169}}$
$=\sqrt{15612+13}=\sqrt{15625}=125$

$\begin{aligned} \sqrt{128} &+\sqrt{160}-\sqrt{16} \\ &=\sqrt{4 \times 4 \times 4 \times 2}+\sqrt{4 \times 4 \times 5 \times 2}-\sqrt{4 \times 4} \\ &=8 \sqrt{2}+4 \sqrt{10}-4 \\ &=11.314+12.649-4 \\ &=19.96 \end{aligned}$