Factor into Prime Factors: Identify the number inside the square root and factor it into prime factors. sqrt(84) can be factored into sqrt(2 * 2 * 3 * 7).Take Out Perfect Square: Recognize that sqrt(2 * 2 * 3 * 7) can be simplified by taking out the square root of the perfect square, which is 2 * 2. This gives us 2 * sqrt(3 * 7).Multiply Known Square Root: Simplify the expression by multiplying the known square root. 2 * sqrt(21) is the simplified form of sqrt(84).Check for Simplification: Check the final answer for any possible simplification. Since 21 is not a perfect square and has no factors that are perfect squares, the expression 2 * sqrt(21) is already in its simplest form.

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$\sqrt{84}$

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Algebra 2

Evaluate rational exponents

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\sqrt{84}

Factor into Prime Factors: Identify the number inside the square root and factor it into prime factors. $\sqrt{84}$ can be factored into $\sqrt{2 \times 2 \times 3 \times 7}$ .
Take Out Perfect Square: Recognize that $\sqrt{2 \times 2 \times 3 \times 7}$ can be simplified by taking out the square root of the perfect square, which is $2 \times 2$ . This gives us $2 \times \sqrt{3 \times 7}$ .
Multiply Known Square Root: Simplify the expression by multiplying the known square root. $2 \times \sqrt{21}$ is the simplified form of $\sqrt{84}$ .
Check for Simplification: Check the final answer for any possible simplification. $\newline$ Since $21$ is not a perfect square and has no factors that are perfect squares, the expression $2 \times \sqrt{21}$ is already in its simplest form.