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Find the simplified product of the following square roots. $\newline$ $\sqrt{63} \times \sqrt{7}$

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Multiply radical expressions

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Q. Find the simplified product of the following square roots.

\newline

\sqrt{63} \times \sqrt{7}

Find Prime Factorization: Find the prime factorization of $63$ which is $3^2 \times 7$ .
Simplify Square Root: Since $\sqrt{63}$ is the same as $\sqrt{3^2 \times 7}$ , we can simplify it to $3\sqrt{7}$ .
Multiply Expressions: Now multiply $3\sqrt{7}$ by $\sqrt{7}$ .
Calculate Result: $3\sqrt{7} \times \sqrt{7}$ equals $3 \times 7$ because the square root of $7$ times itself is just $7$ .
Calculate Result: $3\sqrt{7} \times \sqrt{7}$ equals $3 \times 7$ because the square root of $7$ times itself is just $7$ .So, the final answer is $3 \times 7$ which is $21$ .

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