Question

write the following product in simplest form.\\(sqrt{72} cdot sqrt{63}\\)\\(sqrt{72} cdot sqrt{63} = square\\)\\(\text{(simplify your answer. type an exact answer, using radicals as needed.)}\\)

Explanation:

Step1: Combine the square roots

$\sqrt{72} \cdot \sqrt{63} = \sqrt{72 \times 63}$

Step2: Factor into perfect squares

$72=36\times2$, $63=9\times7$, so $\sqrt{36\times2\times9\times7}$

Step3: Separate perfect square radicals

$\sqrt{36} \times \sqrt{9} \times \sqrt{2\times7}$

Step4: Evaluate perfect square roots

$6 \times 3 \times \sqrt{14}$

Step5: Multiply the constants

$18\sqrt{14}$

Answer:

$18\sqrt{14}$