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Perform the multiplication and present the answer in the most simplified form. $\newline$ $\sqrt{72}\times\sqrt{8}$

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Multiply radical expressions

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Q. Perform the multiplication and present the answer in the most simplified form.

\newline

\sqrt{72}\times\sqrt{8}

Find Prime Factorization: Find the prime factorization of $72$ and $8$ . $72$ is $2^3 \times 3^2$ and $8$ is $2^3$ .
Combine Square Roots: Combine the square roots: $\sqrt{72} \times \sqrt{8} = \sqrt{2^3 \times 3^2} \times \sqrt{2^3}.$
Multiply Square Roots: Multiply the square roots: $\sqrt{2^3 \times 3^2 \times 2^3} = \sqrt{2^6 \times 3^2}$ .
Simplify Square Root: Simplify the square root by taking out the perfect squares: $\sqrt{2^6 \times 3^2} = 2^3 \times 3 = 8 \times 3$ .
Calculate Final Product: Calculate the final product: $8 \times 3 = 24$ .

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