Question

Find the square root of the following number by the prime factorisation method.
$7744$

Answer 1

The factors of $7744$ is,

$7744=2\times 2\times 2\times 2\times 2\times 2\times 11\times 11$

Take square root both sides,

$\sqrt{7744}=\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 11\times 11}$

$=\sqrt{2^6\times {11}^2}$

$=\sqrt{{\left({\left(2\right)}^3\times 11\right)}^2}$

$=8\times 11$

$=88$

Therefore, the square root of 7744 is 88.