Answer:
[tex]-2\sqrt{20}-\sqrt{125}=-9\sqrt{5}[/tex]
Step-by-step explanation:
Given : expression [tex]-2\sqrt{20}-\sqrt{125}[/tex]
We have to write in simplest radical form for the given expression.
Consider the given expression [tex]-2\sqrt{20}-\sqrt{125}[/tex]
Prime factorization is a way of writing a number as the product of its primes.
Thus, 20 can be written as 2 × 2 × 5
[tex]-2\sqrt{20}[/tex] can be written as [tex]=-2\sqrt{2^2\cdot \:5}[/tex]
Apply radical rule, [tex]\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}[/tex] , we get,
[tex]-2\cdot 2\sqrt{5}=-4\sqrt{5}[/tex]
Also, 125 can be written as 5 × 5 × 5
[tex]\sqrt{125}[/tex] can be written as [tex]=\sqrt{5^3}[/tex]
Apply radical rule, [tex]\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}[/tex] , we get,
[tex]\sqrt{125}=5\sqrt{5}[/tex]
The given expression becomes,
[tex]-2\sqrt{20}-\sqrt{125}=-4\sqrt{5}-5\sqrt{5}=-9\sqrt{5}[/tex]
Thus, [tex]-2\sqrt{20}-\sqrt{125}=-9\sqrt{5}[/tex]
