Find the simplified product of the following square roots. sqrt63*sqrt7

Find Prime Factorization: Find the prime factorization of 63 which is 3^2 * 7.Simplify Square Root: Since sqrt63 is the same as sqrt(3^2 * 7), we can simplify it to 3sqrt7.Multiply Expressions: Now multiply 3sqrt7 by sqrt7.Calculate Result: 3sqrt7 * sqrt7 equals 3 * 7 because the square root of 7 times itself is just 7.So, the final answer is 3 * 7 which is 21.

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

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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 $21$ .