Which one of the following numbers is a perfect square? 722,363,5778,625

(A) 722

(B) 5778

(C) 363

(D) 625

Given:

Given numbers are 722, 363, 5778 and 625.

To do:

We have to find which of the given numbers is a perfect square.

Solution:

Prime factorisation of 722 is,

$722=2\times19\times19=2\times(19)^2$

$\sqrt{722}=\sqrt{2\times(19)^2}$

$=19\sqrt{2}$

So, 722 is not a perfect square.

Prime factorisation of 5778 is,

$5778=2\times3\times3\times3\times107$

$\sqrt{5778}=\sqrt{2\times3\times3\times3\times107}$

$=3\sqrt{2\times3\times107}$

 So, 5778 is not a perfect square.

Prime factorisation of 363 is,

$363=3\times11\times11$

$\sqrt{363}=\sqrt{3\times11\times11}$

$=11\sqrt{3}$

 So, 363 is not a perfect square.

Prime factorisation of 625 is,

$625=5\times5\times5\times5$

$\sqrt{625}=\sqrt{5\times5\times5\times5}$

$=\sqrt{5^2\times5^2}$

$=5\times5$

$=25$ 

So, 625 is a perfect square.

Tutorialspoint

Updated on: 10-Oct-2022

78 Views

Kickstart Your Career

Get certified by completing the course

Get Started