Simplify. sqrt 294 ______

Prime Factorization: sqrt(294) Let's do the prime factors of the radicand. Prime factorization of a number is the product of its primes. sqrt(294) = sqrt(2 * 3 * 7 * 7)Group Identical Factors: sqrt(2 * 3 * 7 * 7) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(2 * 3 * 7 * 7) = sqrt(2 * 3 * 7^2)Product Property of Radicals: sqrt(2 * 3 * 7^2) Product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(2 * 3 * 7^2) = sqrt(7^2) * sqrt(2 * 3)Square Root Cancellation: sqrt(294) = sqrt(7^2) * sqrt(2 * 3) Square and square root cancel each other out. sqrt(7^2) * sqrt(2 * 3) = 7 * sqrt(2 * 3) = 7sqrt(6)

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Simplify. $\newline$ $\sqrt{294}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{294}

Prime Factorization: $\sqrt{294}$ $\newline$ Let's do the prime factors of the radicand. $\newline$ Prime factorization of a number is the product of its primes. $\newline$ $\sqrt{294} = \sqrt{2 \times 3 \times 7 \times 7}$
Group Identical Factors: $\sqrt{2 \times 3 \times 7 \times 7}$ $\newline$ Now, group the identical factors. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{2 \times 3 \times 7^2}$
Product Property of Radicals: $\sqrt{2 \times 3 \times 7^2}$ $\newline$ Product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{2 \times 3 \times 7^2} = \sqrt{7^2} \times \sqrt{2 \times 3}$
Square Root Cancellation: $\sqrt{294} = \sqrt{7^2} \times \sqrt{2 \times 3}$ $\newline$ Square and square root cancel each other out. $\newline$ $\sqrt{7^2} \times \sqrt{2 \times 3}$ $\newline$ = $7 \times \sqrt{2 \times 3}$ $\newline$ = $7\sqrt{6}$