Question

What is the square root of 15 times the square root of 6?

Answer 1

Hint: To find the value of statement given we will use property of square root. Firstly we will form an equation where we will multiply square root of 15 to square root of 6. Then by the property of square root we will combine both terms inside on square root and multiply them. Finally we will solve it further to get the final answer.

Complete step-by-step solution:
The statement is given as a square root of 15 times the square root of 6 is.
So firstly we will write square root of both terms as:
$\sqrt{15}$, $\sqrt{6}$
Now as the statement suggest we will multiply both term as:
$\sqrt{15}\times \sqrt{6}$….$\left( 1 \right)$
Now as we know the rule:
$\sqrt{a}\times \sqrt{b}=\sqrt{a\times b}$
Apply above rule in equation (1) as:
$\begin{align}
  & \sqrt{15}\times \sqrt{6}=\sqrt{15\times 6} \\
 & \Rightarrow \sqrt{15}\times \sqrt{6}=\sqrt{90} \\
\end{align}$
Next we will simplify the value further by taking out some value outside the square root as:
$\begin{align}
  & \sqrt{15}\times \sqrt{6}=\sqrt{9\times 10} \\
 & \Rightarrow \sqrt{15}\times \sqrt{6}=\sqrt{9}\times \sqrt{10} \\
 & \Rightarrow \sqrt{15}\times \sqrt{6}={{\left( 3 \right)}^{\dfrac{1}{2}\times 2}}\times \sqrt{10} \\
 & \therefore \sqrt{15}\times \sqrt{6}=3\sqrt{10} \\
\end{align}$
So the value is obtained as $3\sqrt{10}$
Hence square root of 15 times the square root of 6 is $3\sqrt{10}$

Note: Square root means the power of the term is halved. When a number is multiplied by itself it gives the square of the number then the number is known as the square root of that square. Some general square roots should be remembered in order to solve such problems. We can use the factorization method as well inside the square root sign for simplifying the values. A perfect square root exists only for a perfect square as then only the value we get is free of the square root sign.