Question

How do you simplify the square root of $40$?

Answer 1

Solve for the square root using prime factorization.

Calculate the square root of the greatest perfect square from the list of all factors of $40$

The factors of $40$ are $1,2,4,5,8,10,20,$and $40$

Say, $A$ equal $2$

The greatest perfect square from the list of all factors of $40$is $4$

Furthermore, $40$divided by $4$ is $10,$

So, $B$equals $10$

Now we have $A$ and$B$ we can get our answer to $40$ in its simplest radical form as follows:

$$\begin{gathered} \Rightarrow \sqrt{40}=A\sqrt{B} \\ \Rightarrow \sqrt{40}=2\sqrt{10} \end{gathered}$$

Hence, the square root of $40$ written in simplified form is $2\sqrt{10}$