Select the correct answer.

What is this expression in simplified form?
[tex]\[
\sqrt{20} + 3 \sqrt{50} - 2 \sqrt{5}
\][/tex]

A. [tex]\(-12 \sqrt{50}\)[/tex]

B. [tex]\(15 \sqrt{2} + 4 \sqrt{5}\)[/tex]

C. [tex]\(2 \sqrt{5} + 5 \sqrt{2}\)[/tex]

D. [tex]\(15 \sqrt{2}\)[/tex]



Answer :

Sure! Let's simplify the given expression step-by-step:

The expression we need to simplify is:
[tex]\[ \sqrt{20} + 3\sqrt{50} - 2\sqrt{5} \][/tex]

First, we need to simplify each term separately.

1. Simplify [tex]\(\sqrt{20}\)[/tex]

We can write 20 as a product of 4 and 5:
[tex]\[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5} \][/tex]

2. Simplify [tex]\(3\sqrt{50}\)[/tex]

We can write 50 as a product of 25 and 2:
[tex]\[ 3\sqrt{50} = 3\sqrt{25 \times 2} = 3 \times \sqrt{25} \times \sqrt{2} = 3 \times 5 \times \sqrt{2} = 15\sqrt{2} \][/tex]

3. Simplify [tex]\(-2\sqrt{5}\)[/tex]

This term is already in simplified form.

Next, we combine all the simplified terms:
[tex]\[ 2\sqrt{5} + 15\sqrt{2} - 2\sqrt{5} \][/tex]

Notice that the terms [tex]\(2\sqrt{5}\)[/tex] and [tex]\(-2\sqrt{5}\)[/tex] cancel each other out:
[tex]\[ 2\sqrt{5} - 2\sqrt{5} = 0 \][/tex]

So, we're left with:
[tex]\[ 15\sqrt{2} \][/tex]

Thus, the simplified form of the expression [tex]\(\sqrt{20} + 3\sqrt{50} - 2\sqrt{5}\)[/tex] is:
[tex]\[ 15\sqrt{2} \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{D. \ 15 \sqrt{2}} \][/tex]