Question

8. 3sqrt(50) - 3sqrt(32)

Answer 1

To simplify the expression \( 3\sqrt{50} - 3\sqrt{32} \), we can start by simplifying \( \sqrt{50} \) and \( \sqrt{32} \) individually.

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

2. **Simplifying \( \sqrt{32} \)**:
\[
\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2}
\]
Therefore, \( 3\sqrt{32} = 3 \times 4\sqrt{2} = 12\sqrt{2} \).

Now, we can substitute back into the original expression:
\[
3\sqrt{50} - 3\sqrt{32} = 15\sqrt{2} - 12\sqrt{2}
\]

Combining the like terms:
\[
15\sqrt{2} - 12\sqrt{2} = (15 - 12)\sqrt{2} = 3\sqrt{2}
\]

Thus, the simplified expression is:
\[
\boxed{3\sqrt{2}}
\]