Question

simplify the product.
\\(\sqrt{3} \cdot \sqrt{48}\\)
\\(\sqrt{3} \cdot \sqrt{48} = \\) (type an exact answer, using radicals as needed.)

Explanation:

Apply the product rule for radicals

$$ \sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b} $$

$$ \sqrt{3} \cdot \sqrt{48} = \sqrt{3 \cdot 48} $$

Calculate the product inside the radical

$$ 3 \cdot 48 = 144 $$

$$ \sqrt{3 \cdot 48} = \sqrt{144} $$

Simplify the square root

$$ \sqrt{144} = 12 $$

Answer:

\(\sqrt{3} \cdot \sqrt{48} =\) <blank>12</blank> (Type an exact answer, using radicals as needed.)