Simplify the radical expression sqrt(5) * (2 + 3sqrt(5)) (1 point) 2sqrt(5) + 15; 2sqrt(5) + 5; 25sqrt(2) + 2; 4sqrt(5) - 40

Answer 1

To simplify the expression \(\sqrt{5} \cdot (2 + 3\sqrt{5})\), we will distribute \(\sqrt{5}\) to each term inside the parentheses.

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

Calculating each term:

1. \(\sqrt{5} \cdot 2 = 2\sqrt{5}\)
2. \(\sqrt{5} \cdot 3\sqrt{5} = 3(\sqrt{5} \cdot \sqrt{5}) = 3 \cdot 5 = 15\)

Now, combine these results:

\[ 2\sqrt{5} + 15 \]

Thus, the simplified expression is:

\[ \boxed{2\sqrt{5} + 15} \]