Question

find the square root of 625/121 by factorization method

please tell and don't send only answer please show so how it is solved​

Answer 1

First we will separately find the square roots of 625 and 121

In prime factorization, we split the term such that a number becomes the product of its factors.

625

625 = 125 × 5

625 = 25 × 5 × 5

625 = 5 × 5 × 5 × 5

$\sf \implies \sqrt{ \underline{5 \times 5} \times \underline{5 \times 5}}$

$\sf \implies 5 \times 5$

$\bf \implies 25$

Square root of 625 = 25

121

121 = 11 × 11

$\sf \implies \sqrt{\underline{11 \times 11}}$$\bf = 11$

Square root of 121 is 11.

Therefore,

$\sf \sqrt{ \dfrac{625}{121}} = \dfrac{25}{11}$

I hope you understand this and found it helpful ☺️