Simplify. sqrt 24 ______

Find Prime Factors: sqrt(24) Let's start by finding the prime factors of the radicand (the number inside the square root). Prime factorization of a number is expressing it as the product of its prime factors. sqrt(24) = sqrt(2 * 2 * 2 * 3)Group Identical Factors: sqrt(2 * 2 * 2 * 3) Now, we group the identical factors together. Combine the identical factors by using exponents. sqrt(2 * 2 * 2 * 3) = sqrt(2^2 * 2 * 3)Apply Product Property: sqrt(2^2 * 2 * 3) We apply the product property of radicals, which states that sqrt(a * b) = sqrt(a) * sqrt(b). sqrt(2^2 * 2 * 3) = sqrt(2^2) * sqrt(2 * 3)Simplify Square Root: sqrt(24) = sqrt(2^2) * sqrt(2 * 3) We know that the square root of a square number is just the base of the square. Therefore, sqrt(2^2) simplifies to 2. sqrt(2^2) * sqrt(2 * 3) = 2 * sqrt(6)

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Simplify. $\newline$ $\sqrt{24}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{24}

Find Prime Factors: $\sqrt{24}$ $\newline$ Let's start by finding the prime factors of the radicand (the number inside the square root). $\newline$ Prime factorization of a number is expressing it as the product of its prime factors. $\newline$ $\sqrt{24} = \sqrt{2 \times 2 \times 2 \times 3}$
Group Identical Factors: $\sqrt{2 \times 2 \times 2 \times 3}$ $\newline$ Now, we group the identical factors together. $\newline$ Combine the identical factors by using exponents. $\newline$ $\sqrt{2 \times 2 \times 2 \times 3} = \sqrt{2^2 \times 2 \times 3}$
Apply Product Property: $\sqrt{2^2 \times 2 \times 3}$ $\newline$ We apply the product property of radicals, which states that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ . $\newline$ $\sqrt{2^2 \times 2 \times 3} = \sqrt{2^2} \times \sqrt{2 \times 3}$
Simplify Square Root: $\sqrt{24} = \sqrt{2^2} \times \sqrt{2 \times 3}$ $\newline$ We know that the square root of a square number is just the base of the square. Therefore, $\sqrt{2^2}$ simplifies to $2$ . $\newline$ $\sqrt{2^2} \times \sqrt{2 \times 3} = 2 \times \sqrt{6}$