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How do you find the square root of $ 3600 $ ?

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Last updated date: 24th May 2024
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Answer
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Hint: The square root of the number “n” is defined as the number when multiplied by itself and equals to “n”. For example, the square root of $ \sqrt 9 = \sqrt {{3^2}} = 3 $ First we will find the prime factorisation by prime factorization and then with it will find square-root.

Complete step-by-step answer:
Factorization of $ 3600 $ –
Factors $ 3600 = 60 \times 60 $
According to definition- when the same number is multiplied twice, we can write it as the square of the number. So here we will not find further its prime factors
 $ 3600 = {60^2} $
Take square-root on both the sides of the equations –
 $ \sqrt {3600} = \sqrt {{{60}^2}} $
Square and square-root cancel each other on the right hand side of the equation-
\[ \Rightarrow \sqrt {3600} = 60\]
Hence, the square root of $ 3600 $ is $ 60 $
So, the correct answer is “60”.

Note: The squares and the square roots are opposite of each other and so cancel each other. Perfect square number can be defined as the square of an integer, in simple words it is the product of the same integer with itself. For example - $ 25{\text{ = 5 }} \times {\text{ 5, 25 = }}{{\text{5}}^2} $ , generally it is symbolized by n to the power two i.e. $ {n^2} $ . The perfect square is the number which can be expressed as the product of the two equal integers. For example: $ 9 $ , it can be expressed as the product of equal integers. $ 9 = 3 \times 3 $