Question

What is the sum of three radical 5 + 5 radical 20

Answer 1

To simplify the expression \( 3\sqrt{5} + 5\sqrt{20} \), we start by simplifying \( \sqrt{20} \):

\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
\]

Now, we substitute \( \sqrt{20} \) back into the expression:

\[
5\sqrt{20} = 5 \times 2\sqrt{5} = 10\sqrt{5}
\]

Now we can rewrite the original expression:

\[
3\sqrt{5} + 5\sqrt{20} = 3\sqrt{5} + 10\sqrt{5}
\]

Next, we combine the like terms:

\[
3\sqrt{5} + 10\sqrt{5} = (3 + 10)\sqrt{5} = 13\sqrt{5}
\]

Thus, the final sum is:

\[
\boxed{13\sqrt{5}}
\]