Question

What is −2√20 − √125 in simplest radical form? Enter your answer in the box.

Answer 1

Solution:

The simplified form of the radical expression is $-9\sqrt5$

Explanation:

We have been given the radical expression $-2\sqrt{20}-\sqrt{125}$

First of all, we find the factors of 20 and 125

$20=4 \times 5\\\\125 = 25 \times 5$

On plugging these values in the given expression, we get

$-2\sqrt{4 \times 5}-\sqrt{ 25 \times 5}$

We know that square root of 4 is 2 and square root of 25 is 5. Hence, we have

$2\times 2 \sqrt 5 - 5\sqrt 5\\\\-4\sqrt5 - 5\sqrt 5\\\\-9\sqrt5$

Therefore, the simplified form of the radical expression is $-9\sqrt5$

Answer 2

Answer:

$-9\sqrt{5}$

Step-by-step explanation:

We have:

$-2\sqrt{20} -\sqrt{125}$

Now, we need to transform each sub-radical number in another pair of numbers that allow us to simplify each radical into a common radical.

So, we know that 20=4(5), and 125=25(5).

Replacing these in the expression:

$-2\sqrt{4(5)}-\sqrt{25(5)}$; but 4 and 25 have squared roots.

Then:

$-2(2)\sqrt{5} -5\sqrt{5}\\ -4\sqrt{5}-5\sqrt{5}$

Now, we can operate these terms, because they are like terms, that is, they have the same root. Therefore, the simplest radical form is:

$-9\sqrt{5}$