Question

verify whether they are perfect square or not 625​

Answer 1

625 can be written as 25×25

$\sqrt{625 } = \sqrt{25 \times 25} = \sqrt{ {25}^{2} } = 25$

so it is a perfect square

Answer 2

Answer :-

• 625 is a perfect square.

To find :-

• Whether 625 is a perfect square or not.

Step-by-step explanation :-

• Let's use the prime factorisation method for finding out whether 625 is a perfect square or not.

Prime factorisation of 625 :-

$\begin{array}{c | c} \underline{5} & \underline{625} \\ \underline5& \underline{125} \\ \underline5& \underline{ \: \: 25} \\ \underline{5}& \underline{ \: \: \: \: 5} \\ & \: \: \: \: 1\end{array}$

Now,

$\sf625 = 5 \times 5 \times 5 \times 5$

Forming pairs of 2 equal prime factors,

$\sf625 = \underbrace{5 \times 5} \times \underbrace{5 \times 5}$

Conclusion :-

• 625 can be expressed as the product of pairs of equal prime factors,

Therefore :-

• 625 is a perfect square.

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Know more :-

• Now, let's find out the number whose square is 625.

Calculations :-

The given number is 625.

$\rm 625 = \underbrace{5 \times 5} \times \underbrace{5 \times 5}$

$\rm 625 = (5^2) \times (5^2)$

$\rm 625 = (5 \times 5)^2$

$\rm 625 = (25)^2$

• Hence, 25 is the number whose square is 625.

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