Question

How do you simplify $4$ square root $20$?

Answer 1

Hint: We first have to write the statement given in the above question in the form of a mathematical expression. The statement in the above question is $4$ square root $20$. This statement will be mathematically expressed as $4\sqrt{20}$. To simplify it, we have to factorize the number inside the square root and take out the largest perfect square from it. In the expression $4\sqrt{20}$, the number inside the square root is equal to $20$ which is factorized as $2\times 2\times 5$.

Complete step by step solution:
In the above question, we are given the statement $4$ square root $20$, which is to be simplified as. It can be mathematically expressed as
$\Rightarrow E=4\sqrt{20}$
Now, for simplifying it we have to factorize the term inside the square root, or the radical. Inside the radical, we have $20$, which can be factorized as $20=2\times 2\times 5$. Therefore, the above expression can also be written as
$\begin{align}
  & \Rightarrow E=4\sqrt{2\times 2\times 5} \\
 & \Rightarrow E=4\sqrt{{{2}^{2}}\times 5} \\
\end{align}$
Now, from the laws of radicals we know that $\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$. So the above expression can be written as
$\Rightarrow E=4\sqrt{{{2}^{2}}}\sqrt{5}$
We know that the square and the square root cancel each other. Therefore, the given expression finally becomes
$\begin{align}
  & \Rightarrow E=4\times 2\sqrt{5} \\
 & \Rightarrow E=8\sqrt{5} \\
\end{align}$
Hence, the given expression is simplified as $8\sqrt{5}$.

Note:
While simplifying the radical, do not forget the factor of $4$, which is present in the given expression behind the radical. Also, by simplification, the question does not mean to calculate the value of the expression in the decimal form. We only need to reduce the number inside the bracket to the lowest possible factor.