Add the terms if possible.

squareroot 18 + 5 squareroot 2

Select the correct choice below and fill in any answer boxes within your choice.

A. 18 +512 = blank
B. The terms cannot be simplified.

1 answer

To simplify the expression \(\sqrt{18} + 5\sqrt{2}\), we first simplify \(\sqrt{18}\):

\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \]

Now we can rewrite the original expression:

\[ \sqrt{18} + 5\sqrt{2} = 3\sqrt{2} + 5\sqrt{2} \]

Next, we can combine the like terms:

\[ 3\sqrt{2} + 5\sqrt{2} = (3 + 5)\sqrt{2} = 8\sqrt{2} \]

Thus, the simplified expression is \(8\sqrt{2}\).

The correct choice is:

B. The terms cannot be simplified.

However, since we were able to combine and simplify the terms to \(8\sqrt{2}\), the correct answer should acknowledge that simplification was possible, leading to an expression in its simplest form. The original phrasing of option B seems to suggest no simplification could occur, but in summary, we see that \(8\sqrt{2}\) is indeed a simplified result from the original expression.