Question

What is −220−−√−125−−−√ in simplest radical form?

Answer 1

$-2 \sqrt{20} - \sqrt{125} =-2 \sqrt{4\times5} -\sqrt{25\times5} \\ \\ =-4\sqrt{5}-5\sqrt{5}=-9\sqrt{5} \\ \\ \therefore -2 \sqrt{20} - \sqrt{125}=-9\sqrt{5}$

Answer 2

Answer:

$-2\sqrt{20}-\sqrt{125}=-9\sqrt{5}$

Step-by-step explanation:

Given : expression  $-2\sqrt{20}-\sqrt{125}$

We have to write in simplest radical form for the given expression.

Consider the given expression  $-2\sqrt{20}-\sqrt{125}$

Prime factorization is a way of writing a number as the product  of its primes.

Thus, 20 can be written as 2 × 2 × 5

$-2\sqrt{20}$ can be written as $=-2\sqrt{2^2\cdot \:5}$

Apply radical rule, $\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$ , we get,

$-2\cdot 2\sqrt{5}=-4\sqrt{5}$

Also, 125 can be written as 5 × 5 × 5

$\sqrt{125}$ can be written as $=\sqrt{5^3}$

Apply radical rule, $\sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$ , we get,

$\sqrt{125}=5\sqrt{5}$

The given expression becomes,

$-2\sqrt{20}-\sqrt{125}=-4\sqrt{5}-5\sqrt{5}=-9\sqrt{5}$

Thus,  $-2\sqrt{20}-\sqrt{125}=-9\sqrt{5}$