Question

What is the value of $\sqrt {0.09} $?
A. $0.3$
B. $0.03$
C. $0.33$
D. $0.94$

Answer 1

Hint: This is a very simple problem, so let’s first see what’s inside under the square root.
Whatever number is given under the square root just see if you can simplify into fractional numbers, instead of solving in the decimals better solve in terms of fractions. We already know that 9 is a perfect square but the given number is in decimals which is 0.09.

Complete step-by-step solution:
Convert the decimal into fractional form which is given below:
$ \Rightarrow \sqrt {0.09} = \sqrt {\dfrac{9}{{100}}} $
Here the numerator 9 is a perfect square and also the denominator 100 is a perfect square.
$ \Rightarrow \sqrt {\dfrac{9}{{100}}} = \sqrt {\dfrac{{{3^2}}}{{{{10}^2}}}} $
As 9 is a square of 3 and 100 is a square of 10.
$ \Rightarrow \sqrt {\dfrac{9}{{100}}} = \dfrac{3}{{10}}$
$ \Rightarrow \sqrt {0.09} = 0.3$
Hence the value of $\sqrt {0.09} $ is $0.3$

Option A is the correct answer.

Note: This problem can also be done in another method.
Instead of solving the problem in terms of fractions this can also be done in decimals as well.
Consider $\sqrt {0.09} $ where here 0.09 can be written as 0.3*0.3 as below:
$ \Rightarrow \sqrt {0.09} = \sqrt {0.3 \times 0.3} $
$ \Rightarrow \sqrt {0.09} = \sqrt {{{0.3}^2}} $
$ \Rightarrow \sqrt {0.09} = 0.3$
Hence the final answer doesn’t change in any method.