Question

How do you simplify the square root of 2 times the square root of 15?

Answer 1

Hint: First of all, write the language given in the above problem in mathematical terms. In the above problem, it is given that we have to simplify the square root of 2 (which in mathematical term is $\sqrt{2}$) times (meaning multiplied by) the square root of 15 (which in mathematical term is $\sqrt{15}$) . Then we are going to multiply $\sqrt{2}$ by $\sqrt{15}$. And then simplify this product to get the answer.

Complete step by step answer:
We have given above that we have to simplify:
“ the square root of 2 times the square root of 15”
First of all, we are going to do the mathematical conversion of the above statement. The mathematical conversion of the square root of 2 is $\sqrt{2}$ and the mathematical conversion of the square root of 15 is $\sqrt{15}$. Now, we are asked to do the multiplication of $\sqrt{2}\mathrm{\&}\sqrt{15}$ we get,
$\sqrt{2}\times \sqrt{15}$
Also, we know that the product of two square root terms is equal to:
$\begin{array}{rl}& \sqrt{a}\times \sqrt{b}\\ & =\sqrt{a\times b}\\ & =\sqrt{ab}\end{array}$
So, using the above relation in $\sqrt{2}\times \sqrt{15}$ we get,
$\begin{array}{rl}& \sqrt{2\times 15}\\ & =\sqrt{30}\end{array}$
Hence, we have simplified the square root of 2 times the square root of 15 as $\sqrt{30}$ or we can write the square root of 2 times the square root of 15 is equal to the square root of 30.

Note:
To simplify the above expression we should know how to write the square root of any number and also we should know how two terms written in square root are multiplied. Also, in the above problem, we cannot further simplify $\sqrt{30}$ because there is no factor of 30 which is a perfect square. If after multiplication of the square roots, we will get a number whose one of the factors is a square of some number then we can take the square root of that factor. For e.g. let us suppose we would have got $\sqrt{45}$ as the result of multiplication then we can take 9 out from 45 and we are left with:
$\begin{array}{rl}& \sqrt{5\times 9}\\ & =3\sqrt{5}\end{array}$