Question

Find the pairs of numbers in which square of one number is square root of the other number.

• A. $\{4,256\}$
• B. $\{\sqrt{3},9\}$
• C. $\{5,25\}$
• D. $\{\sqrt{2}\times \sqrt{5},100\}$

Answer 1

Answer: (A), (B), (D)

$\{\sqrt{2}\times \sqrt{5},100\}$

We require pairs of numbers for which square of one number is square root of the other number.

For $\{4,256\},$

$4^2=16$

$\sqrt{256}=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2$
$\Rightarrow \sqrt{256}=(2\times 2\times 2\times 2)\times (2\times 2\times 2\times 2)$
$\Rightarrow \sqrt{256}={16}^2$

$\therefore$ This is a possible pair.

Simlarly, other such pair is: $\{\sqrt{3},9\}$
$\Rightarrow (\sqrt{3}{)}^2=3=\sqrt{9}$

Similiarly, $\{\sqrt{2}\times \sqrt{5},100\}\Rightarrow (\sqrt{2}\times \sqrt{5}{)}^2=(\sqrt{10}{)}^2=10=\sqrt{100}$