Question

add.

\\2\sqrt{32} + 3\sqrt{28}\\

\\2\sqrt{32} + 3\sqrt{28} = \box\\
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

⚡ Using what you learned: Simplifying radical expressions

Step 1: Simplify the first radical term

Find the largest perfect square factor of \(32\):

$$ 32 = 16 \times 2 $$

Simplify the term:

$$ 2\sqrt{32} = 2\sqrt{16 \times 2} = 2 \times 4\sqrt{2} = 8\sqrt{2} $$

Step 2: Simplify the second radical term

Find the largest perfect square factor of \(28\):

$$ 28 = 4 \times 7 $$

Simplify the term:

$$ 3\sqrt{28} = 3\sqrt{4 \times 7} = 3 \times 2\sqrt{7} = 6\sqrt{7} $$

Step 3: Combine the simplified terms

Combine the two simplified parts:

$$ 8\sqrt{2} + 6\sqrt{7} $$

Since the radicands (\(2\) and \(7\)) are different, these terms cannot be simplified further.

Answer:

$$ 8\sqrt{2} + 6\sqrt{7} $$