Question

Add the following terms if possible.

3 squareroot 50 + 5squareroot 32

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. 31/50 +5132 = blank (Please type an exact answer, using radicals as needed.)
B. The radicals cannot be combined.

Answer 1

To combine the terms \(3\sqrt{50} + 5\sqrt{32}\), we first need to simplify the square roots.

1. **Simplify \(\sqrt{50}\)**:
\[
\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}
\]
Therefore,
\[
3\sqrt{50} = 3 \cdot 5\sqrt{2} = 15\sqrt{2}
\]

2. **Simplify \(\sqrt{32}\)**:
\[
\sqrt{32} = \sqrt{16 \cdot 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}
\]
Thus,
\[
5\sqrt{32} = 5 \cdot 4\sqrt{2} = 20\sqrt{2}
\]

Now we can combine the terms:
\[
3\sqrt{50} + 5\sqrt{32} = 15\sqrt{2} + 20\sqrt{2} = (15 + 20)\sqrt{2} = 35\sqrt{2}
\]

Since we have a single term now, we can choose:

**A.** \(35\sqrt{2}\)

The answer is:
**35\sqrt{2}**