Question

What is the sum of the following expression?

2√108 + √48 + 5√27


(1 point)
Responses

8183−−−√
8 square root of 183

133–√
13 square root of 3

31183−−−√
31 square root of 183

313–√

Answer 1

To find the sum of the expression \( 2\sqrt{108} + \sqrt{48} + 5\sqrt{27} \), we will simplify each term individually and then combine them.

1. **Simplifying \( \sqrt{108} \)**:
\[
\sqrt{108} = \sqrt{36 \times 3} = \sqrt{36} \cdot \sqrt{3} = 6\sqrt{3}
\]
Therefore,
\[
2\sqrt{108} = 2 \cdot 6\sqrt{3} = 12\sqrt{3}
\]

2. **Simplifying \( \sqrt{48} \)**:
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3}
\]

3. **Simplifying \( 5\sqrt{27} \)**:
\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3}
\]
Therefore,
\[
5\sqrt{27} = 5 \cdot 3\sqrt{3} = 15\sqrt{3}
\]

Now we can combine all the simplified terms:
\[
2\sqrt{108} + \sqrt{48} + 5\sqrt{27} = 12\sqrt{3} + 4\sqrt{3} + 15\sqrt{3}
\]
\[
= (12 + 4 + 15)\sqrt{3} = 31\sqrt{3}
\]

Thus, the sum of the expression is:
\[
\boxed{31\sqrt{3}}
\]