Question

How do you simplify $\dfrac{\sqrt{35}}{\sqrt{7}}$?

Answer 1

Hint: In this question we have a fraction which as terms in the square root. We will use the property of square roots to simplify the expression to get the required solution. We will first express the term $35$ in its factors and cancel it with the term in the denominator.

Complete step-by-step answer:
We have the expression given to us as:
$\Rightarrow \dfrac{\sqrt{35}}{\sqrt{7}}$
Now will write the term $35$ as a product of its factors. Since the only way to express $35$ is by the product of $7$ and $5$ therefore, we can write the expression as:
$\Rightarrow \dfrac{\sqrt{7\times 5}}{\sqrt{7}}$
Now we have the terms in the square root, we can split the term using the property of square root which is $\sqrt{a\times b}=\sqrt{a}\times \sqrt{b}$.
On using this property in the numerator, we get:
$\Rightarrow \dfrac{\sqrt{7}\times \sqrt{5}}{\sqrt{7}}$
On cancelling the similar terms in the numerator and denominator, we get:
$\Rightarrow \sqrt{5}$
As the root value cannot be simplified any further, it is the required simplified value.

Note: In this question we had the terms in the form of square root. The square root of a term represents that value which has to be multiplied by itself to get the original value. A term in square root can also be represented in the form of an exponent as ${{x}^{\dfrac{1}{2}}}$. It is to be remembered that when taking the square root of a number there are two answers, one which is the square root in positive and one which is the square root in negative.