Question

write the following product in simplest form.
\\(\sqrt{72} \cdot \sqrt{63}\\)

\\(\sqrt{72} \cdot \sqrt{63} = \square\\)
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Use property of square roots

Recall that $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$. So, $\sqrt{72} \cdot \sqrt{63} = \sqrt{72 \times 63}$.

Step2: Factor the product inside the square root

First, factor 72 and 63: $72 = 36 \times 2$ and $63 = 9 \times 7$. Then $72 \times 63 = 36 \times 2 \times 9 \times 7$.

Step3: Simplify the square root

We know that $\sqrt{36} = 6$, $\sqrt{9} = 3$. So, $\sqrt{36 \times 2 \times 9 \times 7} = \sqrt{36} \times \sqrt{9} \times \sqrt{2 \times 7} = 6 \times 3 \times \sqrt{14}$.

Step4: Multiply the constants

$6 \times 3 = 18$, so we get $18\sqrt{14}$.

Answer:

$18\sqrt{14}$