Question

Find square root of 4225 using prime factor methods ​

Answer 1

Once refer attachment :-

Step - 1 :-

First 4225 Resolve into prime factors Using prime factorisation

$\begin{array}{c|c}\sf5&\sf4225\\ \cline{2-2}\sf5&\sf845\\ \cline{2-2}\sf13&\sf169\\ \cline{2-2}\sf13&\sf13\\ \cline{2-2}&\sf1\end{array}$

It can be written as (5×5)×(13×13)

Step -2 :-

We can observe 5, 13 exists in pairs

Step :- 3

Now ,

$\sf\sqrt{4225}$ = $\sf\sqrt{(5\times5) \times (13\times13)}$

$\sf\sqrt{4225}$ = $\sf\sqrt{(5)^2 \times(13)^2}$

$\sf\sqrt{4225}$ = $\sf\sqrt{(5\times13)^2}$

$\sf\sqrt{4225}$ = 5×13

$\sf\sqrt{4225}$ = 65

So, square root of 4225 is 65

Note :-

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