Question

Simplify.
v45 + 2v20

Answer 1

To simplify the expression \( \sqrt{45} + 2\sqrt{20} \), we can start by simplifying each square root.

1. Simplify \( \sqrt{45} \):
\[
\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \sqrt{5} = 3\sqrt{5}
\]

2. Simplify \( \sqrt{20} \):
\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \sqrt{5} = 2\sqrt{5}
\]

Now, substitute these simplified forms back into the expression:
\[
\sqrt{45} + 2\sqrt{20} = 3\sqrt{5} + 2(2\sqrt{5}) = 3\sqrt{5} + 4\sqrt{5}
\]

Now, combine the terms:
\[
3\sqrt{5} + 4\sqrt{5} = (3 + 4)\sqrt{5} = 7\sqrt{5}
\]

Thus, the simplified expression is:
\[
\boxed{7\sqrt{5}}
\]