Question

Simplify the given surd: $4\sqrt{7}-3\sqrt{252}+5\sqrt{343}$.

Answer 1

The given surds can be simplified as follows:

$4\sqrt{7}-3\sqrt{252}+5\sqrt{343}=4\sqrt{7}-3\sqrt{36\times 7}+5\sqrt{49\times 7}=4\sqrt{7}-(3\times 6\sqrt{7})+(5\times 7\sqrt{7})=4\sqrt{7}-18\sqrt{7}+35\sqrt{7}$

$=\sqrt{7}(4+35-18)=\sqrt{7}(39-18)=21\sqrt{7}$

Hence, $4\sqrt{7}-3\sqrt{252}+5\sqrt{343}=21\sqrt{7}$.