Question

How do you find the square root of $\dfrac{{36}}{{49}}?$

Answer 1

Hint:
Whenever we need to find the square root of any given number, first we need to know or we need to find its prime factors. After finding a suitable prime factor if we multiply then we need to get the same number. But here they have given in fraction from so we can find the square root of numerator and denominator separately and combining we get the same answer.

Complete step by step solution:
Whenever we need to find the square root of any given number, first we need to know or we need to find its prime factors.
Prime numbers are nothing but the numbers which can be divided by $1$ and the number itself. The starting prime numbers are: $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31$ and so on.
In the given question they have asked to find square root of fraction that is $\dfrac{{36}}{{49}}$, whenever we have this type of question we can do in the following form: $\sqrt {\dfrac{m}{n}} = \dfrac{{\sqrt m }}{{\sqrt n }}$ so we can find square root of numerator and denominator separately to get the answer.
Now, we check for prime factor:
$\sqrt {\dfrac{{36}}{{49}}} = \dfrac{{\sqrt {36} }}{{\sqrt {49} }}$
The prime factors for the above is as follows
$ \Rightarrow \dfrac{{\sqrt {36} }}{{\sqrt {49} }} = \dfrac{{\sqrt {2 \times 2 \times 3 \times 3} }}{{\sqrt {7 \times 7} }} = \dfrac{6}{7}$

Therefore, the square root of $\dfrac{{36}}{{49}}$ is $\dfrac{6}{7}$.

Cross verification:
we can do cross verification to check whether we have got the correct answer or not. If we multiply the numerator or the denominator value which we got twice, then if it gives the number equal to the value which they have given in the problem then we can say the answer is correct. Therefore $6 \times 6 = 36$ and $7 \times 7 = 49$, hence the answer is correct.

Note:
The square root can also be found by using a long division method as well. Both the prime factor and long division method gives the correct answer. Only thing is by using the prime factor method you need to know prime numbers to check whether it will divide the number properly or not.