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# How do you simplify the square root of $0.01?$

Last updated date: 21st Mar 2023
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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 first convert the decimal number in the form of a simple fraction and then will find factorisation and then with it will find square-root.

Factorization of $0.01$
convert the above number in the form of simple fraction -
Factors $0.01 = \dfrac{1}{{100}}$
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
$0.01 = \dfrac{1}{{10 \times 10}}$
Take square-root on both the sides of the equations –
$\sqrt {0.01} = \sqrt {\dfrac{1}{{10 \times 10}}}$
The above expression can be re-written as –
$\sqrt {0.01} = \sqrt {\dfrac{1}{{{{10}^2}}}}$
Square and square-root cancel each other on the right hand side of the equation-
$\sqrt {0.01} = \dfrac{1}{{10}}$
Convert the fraction in the form of decimal number –
$\sqrt {0.01} = 0.1$
Hence, the square root of $\sqrt {0.01}$ is $0.1$
So, the correct answer is “0.1”.

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. $9 = 3 \times 3$