Question

Find the square root of 70.56.

Answer 1

Hint – In this question use the concept that the square root of any number $a$ is ${a^{\dfrac{1}{2}}}$. After removing decimal places factorize the numerator part and use the basic exponent properties to get the answer.
Complete step-by-step answer:
Given number is 70.56
Now we have to find out the square root of 70.56.
$ \Rightarrow \sqrt {70.56} = \sqrt {\dfrac{{7056}}{{100}}} = {\left( {\dfrac{{7056}}{{100}}} \right)^{\dfrac{1}{2}}}$...................... (1)
Now factorize 7056 we have,
$7056 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7 \times 7 = {2^4} \times {3^2} \times {7^2}$
Now substitute this value in equation (1) we have,
 \[ \Rightarrow \sqrt {70.56} = {\left( {\dfrac{{7056}}{{100}}} \right)^{\dfrac{1}{2}}} = {\left( {\dfrac{{{2^4} \times {3^2} \times {7^2}}}{{{{10}^2}}}} \right)^{\dfrac{1}{2}}} = \dfrac{{{2^{4 \times \dfrac{1}{2}}} \times {3^{2 \times \dfrac{1}{2}}} \times {7^{2 \times \dfrac{1}{2}}}}}{{{{10}^{2 \times \dfrac{1}{2}}}}}\]
Now simplify the above equation we have,
\[ \Rightarrow \sqrt {70.56} = \dfrac{{{2^{4 \times \dfrac{1}{2}}} \times {3^{2 \times \dfrac{1}{2}}} \times {7^{2 \times \dfrac{1}{2}}}}}{{{{10}^{2 \times \dfrac{1}{2}}}}} = \dfrac{{{2^2} \times 3 \times 7}}{{10}} = \dfrac{{84}}{{10}} = 8.4\]
So this is the required square root of 70.56.

Note – When a number is multiplying itself the product refers to the square number. Further the number is the number root. Thus we get perfect square roots for a perfect square number only. An odd perfect square will have an odd square root only.