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]
