Question

Find the square root of 225 by prime Factrorisation method ​

Answer 1

$step \: 1$

$prime \: factor \: of \: 225$

$step \: 2$

$225 = 5 \times 5 \times 3 \times 3$

$step \: 3$

$\sqrt{225 = \sqrt{5 \times 5 \times 3 \times 3} }$

$step \: 4$

$\sqrt{225 = 5 \times 3}$

$step \: 5$

$5 \times 3 = 15$

$step \: 6$

$therefore \: the \: square \: root \: of \: 225 \\ is \: 15$

HOPE IT WILL HELP YOU................

Answer 2

$\underline{\underline{\bold{Answer}}}$

15.

$\huge\bold{Explanation}$

According to the question, we have to find the square root of the given number. there are two method to find the square root of the given number -

● Prime factorisation method

● Long division method

$\sf{Let\:find\:the\:square\:root\:by\:using\:1st\:method}$

$\sf{Let\:find\:the\:prime\:factors\:of\:225.}$

$\begin{array}{r | l} 3 & 225 \\ \cline{2-2} 3 & 75 \\ \cline{2-2} 5 & 25 \\ \cline{2-2} 5 & 5 \\ \cline{2-2} & 1 \end{array}$

225 = 3 × 3 × 5 × 5

$\sf{According\:to\:the\:question,}$

$\sqrt{225} = \sqrt{3\times 3\times 5\times 5}$

We know that , to find the square root of any number we just pair it out...

$\implies{\sqrt{225} = 3\times 5}$

So, the square root of the number is, the product of 3 and 5

$\implies{3\times 5 = 15}$

$\boxed{\boxed{\sf{\therefore{\sqrt{225} = 15}}}}$