Question

What is the square root of 20 times the square root of 15?

Answer 1

Hint: For solving this question you should know how to calculate the square root of any term with its multiplication also. So, in this question we will take square root and then will take the multiplication of both and then we will solve this as a procedure. Thus, we will get the answer for this.

Complete step-by-step solution:
According to the question we have to calculate the square root of 20 times the square root of 15. It means first we take the square root of both and then we multiply both. We calculate the square root of any terms if it is a positive term, then it is very much easy and can be calculated directly but if it is a negative term then it is easy to find the square root of that but in this the value will be imaginary and this value does not exist. And if we calculate the square root of a positive number with decimal then it will also be very tough because it is solved by Heron's formula.
So, according to our question we have to calculate the square root of 20 times $\sqrt{15}$. So, the square root of,
$\begin{align}
  & y=\sqrt{{{x}^{2}}} \\
 & \Rightarrow y=x \\
\end{align}$
So, according to our question,
Square root of 20 = $\sqrt{20}$
Square root of 15 = $\sqrt{15}$
Now as according to the question,
$\begin{align}
  & \sqrt{20}.\sqrt{15} \\
 & =\sqrt{4.5}.\sqrt{15} \\
\end{align}$
Since we know that $\sqrt{a.b}=\sqrt{a}.\sqrt{b}$
Hence,
$\begin{align}
  & \sqrt{4.5}.\sqrt{15}=\sqrt{4}.\sqrt{5}.\sqrt{3}.\sqrt{5} \\
 & \Rightarrow \sqrt{4.5}.\sqrt{15}=2{{\left( \sqrt{5} \right)}^{2}}.\sqrt{3} \\
 & \Rightarrow \sqrt{4.5}.\sqrt{15}=2.5.\sqrt{3} \\
 & \Rightarrow \sqrt{4.5}.\sqrt{15}=10\sqrt{3} \\
\end{align}$
So, the square root of 20 times of the square root of 15 is equal to $10\sqrt{3}$.

Note: During the calculation of this question, you should be careful about the square root because if the value will be negative then it will be solved by a different method and if positive then form a different method. And take the reciprocal and make the denominator complete if any negative value is given as a fractional form.