Question

What is the sum of the following expression two radical 108 + radical 48 + 5√27

Answer 1

To simplify the expression \( 2\sqrt{108} + \sqrt{48} + 5\sqrt{27} \), we will simplify each square root term.

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

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

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

Now we can substitute these simplified forms back into the original expression:
\[
2\sqrt{108} + \sqrt{48} + 5\sqrt{27} = 12\sqrt{3} + 4\sqrt{3} + 15\sqrt{3}
\]

Next, we can combine the like terms:
\[
12\sqrt{3} + 4\sqrt{3} + 15\sqrt{3} = (12 + 4 + 15)\sqrt{3} = 31\sqrt{3}
\]

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