Find the square root:
(i) 625
(ii) 1225

Given :

The given numbers are:

(i) 625 (ii) 1225

To do :

We have to find the square roots of given numbers.

Solution :

(i) Prime factorisation of 625 is,

$625 = 5\times 5\times 5\times 5$

$625 = (5\times 5)\times (5\times 5)$

$625 = (25\times 25)$

Therefore,

$625 = (25)^2$

$\sqrt{625}=\sqrt{(25)^2}$

                    $= 25$

Therefore, the value of $\sqrt{625}$ is 25.

(ii) Prime factorisation of 1225 is,

$1225 = 5\times 5\times 7\times 7$

$1225 = (5\times 5)\times (7\times 7)$

$1225 = (5^2\times 7^2)$

$1225 = (5\times 7)^2$

Therefore,

$1225 = (35)^2$

$\sqrt{1225}=\sqrt{(35)^2}$

                    $= 35$

Therefore, the value of $\sqrt{1225}$ is 35.

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Updated on: 10-Oct-2022

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