Question

Add and subtract the following terms, if possible.

2 squareroot 8 - squareroot 32 + 2 squareroot 72- squareroot 75

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. 2 squareroot 8 - squareroot 32 + 2 squareroot 72- squareroot 75 = blank (Please type an exact answer, using radicals as needed)
B. The radicals cannot be combined.

Answer 1

Let's simplify each term before combining them:

1. **\(2 \sqrt{8}\)**:
\[
2 \sqrt{8} = 2 \sqrt{4 \cdot 2} = 2 \cdot 2 \sqrt{2} = 4\sqrt{2}
\]

2. **\(-\sqrt{32}\)**:
\[
-\sqrt{32} = -\sqrt{16 \cdot 2} = -4\sqrt{2}
\]

3. **\(2 \sqrt{72}\)**:
\[
2 \sqrt{72} = 2 \sqrt{36 \cdot 2} = 2 \cdot 6 \sqrt{2} = 12\sqrt{2}
\]

4. **\(-\sqrt{75}\)**:
\[
-\sqrt{75} = -\sqrt{25 \cdot 3} = -5\sqrt{3}
\]

Now we can combine the like terms:

Combining the terms involving \(\sqrt{2}\):
\[
4\sqrt{2} - 4\sqrt{2} + 12\sqrt{2} = (4 - 4 + 12) \sqrt{2} = 12\sqrt{2}
\]

And we still have \(-5\sqrt{3}\) remaining, so the complete expression is:
\[
12\sqrt{2} - 5\sqrt{3}
\]

Thus, the answer is:
**A. \(2 \sqrt{8} - \sqrt{32} + 2 \sqrt{72} - \sqrt{75} = 12\sqrt{2} - 5\sqrt{3}\)**.