Question

add.

(2\sqrt{45} + 3\sqrt{75})

(2\sqrt{45} + 3\sqrt{75} = \square)
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

⚡ Using what you learned: Roots and Radicals

Step 1: Simplify the first radical term

$$ 2\sqrt{45} = 2\sqrt{9 \cdot 5} = 2 \cdot 3\sqrt{5} = 6\sqrt{5} $$

Step 2: Simplify the second radical term

$$ 3\sqrt{75} = 3\sqrt{25 \cdot 3} = 3 \cdot 5\sqrt{3} = 15\sqrt{3} $$

Step 3: Combine the simplified terms

$$ 2\sqrt{45} + 3\sqrt{75} = 6\sqrt{5} + 15\sqrt{3} $$

Since the radicands are different, the terms cannot be combined further.

Answer:

\(6\sqrt{5} + 15\sqrt{3}\)