Question

The expression $\sqrt{(\sqrt{56})(\sqrt{126})}$ can be simplified to $a\sqrt b$, where $a$ and $b$ are integers and $b$ is not divisible by any perfect square greater than 1. What is $a+b$?

Answer 1

23

Explanation:

Since 56 is a multiple of 4 and 126 is a multiple of 9, we can factor squares out of both terms, getting $\sqrt{(2\sqrt{14})(3\sqrt{14})}=\sqrt{2\cdot3\cdot14}$. Then, we can factor $2^2$ out of the outer square root to get $2\sqrt{21}$. Thus $a=2$ and $b=21$, yielding $a+b=\boxed{23}$.

Answer 2

23

Explanation:

`\sqrt{√(56)√(126)}=\sqrt{√(7056)}=\sqrt{√(84^2)}\\\\=√(84)=2√(21)\\\\2+21=\bf{23}`