Question

What is -2 sqrt 20 - sqrt 125 in simplest radical form?

Answer 1

`-2√(20)-√(125)=-2√(4\cdot5)-√(25\cdot5)\\\\\text{use}\ √(ab)=√(a)\cdot√(b)\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\=-2\sqrt4\cdot\sqrt5-√(25)\cdot\sqrt5=-2(2)\sqrt5-5\sqrt5\\\\=-4\sqrt5-5\sqrt5=(-4-5)\sqrt5=\boxed{-9\sqrt5}`