Question

How do you simplify $\dfrac{65}{\sqrt{39}}$?

Answer 1

Hint: In order to do this question, first you have to multiply both the numerator and the denominator with the value in the denominator. You do this, so that you don’t have any square root part in the denominator. Next you can check if you can simplify the expression. You can cancel out the factors which are common in both numerator and denominator. Then, you get your final answer.

Complete step by step answer:
The first and the foremost step to solve this question, is to multiply both the numerator and the denominator with the value in the denominator. Here the value in the denominator is square root of 39. By doing this, we can remove any square root terms in the denominator. Therefore, we get
$\Rightarrow \dfrac{65}{\sqrt{39}} \times \dfrac{\sqrt{39}}{\sqrt{39}}$
$\Rightarrow \dfrac{65 \sqrt{39}}{39}$

The next step is to cancel out any factors which are common in both numerator and the denominator. As we can see 13 is the common factor in both numerator and denominator, we can cancel 65 with 5 and 39 with 3, Hence we get the answer as
$\Rightarrow \dfrac{5 \sqrt{39}}{3}$

Therefore, we get the final answer for the question, How do you simplify $\dfrac{65}{\sqrt{39}}$ , as $ \dfrac{5 \sqrt{39}}{3}$

Note: When you get the problems of these kinds, you should first make sure that there is no square root term in the denominator. This makes the simplification easier. Also, be careful while simplifying that is when cancelling out the factors in both the numerator and denominator.