Simplify. sqrt 150 ______

Find Prime Factors: sqrt(150) Let's find 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(150) = sqrt(2 * 3 * 5 * 5)Group and Combine Factors: sqrt(2 * 3 * 5 * 5) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(2 * 3 * 5 * 5) = sqrt(2 * 3 * 5^2)Apply Product Property: sqrt(2 * 3 * 5^2) Product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(2 * 3 * 5^2) = sqrt(2) * sqrt(3) * sqrt(5^2)Cancel Square Root: sqrt(150) = sqrt(2) * sqrt(3) * sqrt(5^2) Square and square root cancel each other out for the term sqrt(5^2). sqrt(2) * sqrt(3) * sqrt(5^2) = sqrt(2) * sqrt(3) * 5Combine and Multiply: sqrt(150) = sqrt(2) * sqrt(3) * 5 Combine the square roots and multiply by 5. sqrt(150) = 5 * sqrt(2 * 3) sqrt(150) = 5 * sqrt(6)

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Simplify. $\newline$ $\sqrt{150}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{150}

Find Prime Factors: $\sqrt{150}$ $\newline$ Let's find 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. $\newline$ $\sqrt{150} = \sqrt{2 \times 3 \times 5 \times 5}$
Group and Combine Factors: $\sqrt{2 \times 3 \times 5 \times 5}$ $\newline$ Now, group the identical factors. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{2 \times 3 \times 5^2}$
Apply Product Property: $\sqrt{2 \times 3 \times 5^2}$ $\newline$ Product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{2 \times 3 \times 5^2} = \sqrt{2} \times \sqrt{3} \times \sqrt{5^2}$
Cancel Square Root: $\sqrt{150} = \sqrt{2} \times \sqrt{3} \times \sqrt{5^2}$ $\newline$ Square and square root cancel each other out for the term $\sqrt{5^2}$ . $\newline$ $\sqrt{2} \times \sqrt{3} \times \sqrt{5^2} = \sqrt{2} \times \sqrt{3} \times 5$
Combine and Multiply: $\sqrt{150} = \sqrt{2} \times \sqrt{3} \times 5$ $\newline$ Combine the square roots and multiply by $5$ . $\newline$ $\sqrt{150} = 5 \times \sqrt{2 \times 3}$ $\newline$ $\sqrt{150} = 5 \times \sqrt{6}$