Question

What is the \[\text{square root of 15 / square root of }5\] ?

Answer 1

Hint: Here in this question we have been asked to find the value of the square root of 15 divided by the square root of 5. To answer this question we will simplify the given expression mathematically and then come to a final conclusion.

Complete step by step answer:
Now considering the question we have been asked to find the value of the square root of 15 divided by the square root of 5.
Now we will write the given expression mathematically as $\dfrac{\sqrt{15}}{\sqrt{5}}$ .
By further simplifying this expression we can write it as $\dfrac{{{15}^{\dfrac{1}{2}}}}{{{5}^{\dfrac{1}{2}}}}$ .
From the basic concepts we know that the basic identity of algebra which is given as $\left( \dfrac{{{a}^{x}}}{{{b}^{x}}} \right)={{\left( \dfrac{a}{b} \right)}^{x}}$ .
Now we need to simplify this using the above discussed point.
After doing that we will have ${{\left( \dfrac{15}{5} \right)}^{\dfrac{1}{2}}}$ .
Now by further simplifying the given expression we will have $\Rightarrow {{3}^{\dfrac{1}{2}}}$ .
Hence we can conclude that the value of the square root of 15 divided by the square root of 3 will be given as $\sqrt{3}$ .

Note: While answering questions of this type we should be sure with the calculations that we are going to perform in between the steps in order to simplify the given expression and come to a final conclusion. This is a very simple and easy question and can be answered in a short span of time accurately. Very few mistakes are possible in questions of this type. Someone can make a calculation mistake in a hurry for an example they can consider ${{\left( \dfrac{15}{5} \right)}^{\dfrac{1}{2}}}=\sqrt{4}$ which leads them to end up having a wrong conclusion.