Question

What is the square root of 40 over 2?

Answer 1

Hint: We need to first assemble the terms one by one because it might create confusion if not done properly. After that we need to find the square root, i.e. the number which when multiplied by itself gives the number whose square root we are trying to find. The term “over” means to divide the quantity we are given by some other quantity given.

Complete step by step solution:
Here, start assembling terms from the right. The term “40 over 2” means we divide the number 40 by 2. If we divide 40 by 2, we will get:
$\dfrac{40}{2}=20$, so 20 is obtained.
Now, the next set of terms is “square root of” the result so obtained.
We have 20 as the result obtained by assembling the previous set of words, so we are required to find the square root of 20. To find the square root of 20 we need to factorize it and take the terms out which are multiplied by itself, which is done as follows:
$\sqrt{20}=\sqrt{2\times2\times5}$
We see here that 2 is repeated twice, so we take that out of the square root and obtain the following expression:
$\sqrt{20}=2\times\sqrt{5}$
$\implies \sqrt{\dfrac{40}{2}}=2\times\sqrt5$
Hence, the result is obtained.

Note: Do not mix the terms. Creating the expression out of mathematical terms is often confusing because the terms get mixed up. Here, the division is done first, and then the square root is taken. One might do it the other way, i.e. first of the square root of 40 and then divide the whole thing by 2 which would be wrong.