Question

How do you find the square root of 208?

Answer 1

Hint: In the above question you were asked to find the square root of 208. So first you have to find the factors of 208 and then you will check if there is any square term. If there is any such square term then you can take that digit out of square root. So let us see how we can solve this problem.

Complete Step by Step Solution:
In the given question we have to find the value of $\sqrt {208}$. So first we will find the factors of $\sqrt {208}$.
 $= \sqrt {4 \times 4 \times 13}$
 $= \sqrt {{4^2} \times 13}$
We can take ${4^2}$ out of the root
 $= 4\sqrt {13}$

Therefore, the square root of 208 is $4\sqrt {13}$.

Additional Information:
The $\sqrt {}$ symbol is known as radical. If a square root of n is given then you can also write $\sqrt n = {n^{\dfrac{1}{2}}}$ , for the cube root of n, it can be written as $\sqrt[3]{n} = {n^{\dfrac{1}{3}}}$ . So the answer to the above question can also be written as in this form but $4\sqrt {13}$ is convenient and easy to understand.

Note:
In the given question we take the factor of 208 and then took the square term which is 4 out of square root. After which we got our answer. Also, we could convert $4\sqrt {13}$ into a fraction, it will give 14.422.