Question

How do you simplify \[\sqrt{74}\] ?

Answer 1

Hint: The approach to this question is pretty simple, you just need to find the factors of the provided number, and then from the list of the number of factors you need to find the perfect squares among them. So, let’s begin.

Complete Step by Step Solution:
Whenever we see a root sign before a radical, we need to find the factors for the following number.
For example, we can assume a number like 50, so when we convert the number into its factors, we get 25 and a 5. Now, when we look upon the list of number of factors, we can eventually see that only 25 is the perfect square which means we get,
 $\Rightarrow {{5}^{2}}=25$
Henceforth, whenever there is a radical, we need to convert it to a whole number instead of any fractional form or decimal form.
But, unfortunately, the number which is provided to us that is 74 will not have any perfect squares in the list of the number of factors that means when we see the factors it’s 2 and 37, none of them is a perfect square.

Henceforth, we cannot simplify the number $\sqrt{74}$.

Note:
There is an alternative way of solving radicals that is we can convert it to an exponent and bring it in the form of the whole number.
For example,
$\Rightarrow \sqrt{81}={{81}^{\dfrac{1}{2}}}={{9}^{2\times \dfrac{1}{2}}}=9$