Question

find by prime factorisation the square root of = 9025...write in explanation in your copy ​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer :-

• The square root of 9025 is 95.

To find :-

• The square root of 9025 by prime factorisation.

Solution :-

• Let's find the square root of 9025!

Prime factorisation of 9025 :-

$\begin{array}{c | c} \underline5 & \underline{9025} \\ \underline5&\underline{1805} \\ \underline{19}&\underline{361} \\ \underline{19}&\underline{19} \\ &1\end{array}$

The given number is 9025. It is a perfect square as it can be expressed as the product of pairs of equal prime factors.

Now :-

$\sf9025 = \underbrace{5 \times 5} \times \underbrace{19 \times 19}$

$\sf9025 = ({5}^{2}) \times ({19}^{2} )$

$\sf9025 = (5 \times 19)^{2}$

$\sf9025 = (95)^{2}$

Hence :-

• The square root of 9025 is 95.

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