Question

Adding /subtracting radicals
4√45+3√245

Answer 1

To simplify the expression \(4\sqrt{45} + 3\sqrt{245}\), we first simplify each radical individually.

1. **Simplifying \( \sqrt{45} \)**:

\[
\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \cdot \sqrt{5} = 3\sqrt{5}
\]

Therefore:
\[
4\sqrt{45} = 4 \cdot 3\sqrt{5} = 12\sqrt{5}
\]

2. **Simplifying \( \sqrt{245} \)**:

\[
\sqrt{245} = \sqrt{49 \times 5} = \sqrt{49} \cdot \sqrt{5} = 7\sqrt{5}
\]

Therefore:
\[
3\sqrt{245} = 3 \cdot 7\sqrt{5} = 21\sqrt{5}
\]

Now, we can combine the two terms:

\[
4\sqrt{45} + 3\sqrt{245} = 12\sqrt{5} + 21\sqrt{5} = (12 + 21)\sqrt{5} = 33\sqrt{5}
\]

Thus, the final result is:

\[
\boxed{33\sqrt{5}}
\]