Question

How do you simplify $\sqrt {49} $?

Answer 1

Hint: The given expression in the question is a square root. A square root of a number is a value which when multiplied by itself, gives the number. For example, let us multiply $2$ by itself. It would give us $2 \times 2 = 4$. So here, $2$ is the square root of $4$.
There are two methods for solving square roots, i.e. by using the perfect square method and by using the prime factorization method. We are going to use the prime factorization method here.

Complete step by step solution:
Given square root is $\sqrt {49} $. The number given within square root is $49$.
We will now break the number $49$ into prime factors, such that
$49 = 7 \times 7$
Now for each pair of factors, we will take one out of the square root sign. Since there is a pair of $7$ we will take one $7$ out of the square root sign. So we will get
$\sqrt {49} = \sqrt {7 \times 7} = 7$
The remaining factors in the square root sign are multiplied together and are kept under the sign only. Since there are no remaining factors, we get a whole number as the answer.

Hence on simplifying $\sqrt {49} $, we get $7$ as the solution.

Note:
We can also use the other way, namely the perfect square method to simplify $\sqrt {49} $. In this method, we have to find a perfect square that divides the number within the square root sign.
The perfect square which divides $49$is $49$ itself as it is already a perfect square. We will now factorise $49$, such that
$49 = 7 \times 7$
We will now reduce $49$,
$\sqrt {49} = \sqrt {7 \times 7} = 7$
Hence, the square root of $\sqrt {49} $ is $7$.