Simplify. sqrt 90 ______

Find Prime Factors: sqrt(90) 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(90) = sqrt(2 * 3 * 3 * 5)Group and Combine Factors: sqrt(2 * 3 * 3 * 5) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(2 * 3 * 3 * 5) = sqrt(2 * 3^2 * 5)Apply Product Property: sqrt(2 * 3^2 * 5) Apply the product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(2 * 3^2 * 5) = sqrt(3^2) * sqrt(2 * 5)Simplify Perfect Square: sqrt(90) = sqrt(3^2) * sqrt(2 * 5) Simplify the square root of the perfect square. Square and square root cancel each other out. sqrt(3^2) * sqrt(2 * 5) = 3 * sqrt(10)

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Simplify. $\newline$ $\sqrt{90}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{90}

Find Prime Factors: $\sqrt{90}$ $\newline$ 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. $\newline$ $\sqrt{90} = \sqrt{2 \times 3 \times 3 \times 5}$
Group and Combine Factors: $\sqrt{2 \times 3 \times 3 \times 5}$ $\newline$ Now, group the identical factors. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{2 \times 3^2 \times 5}$
Apply Product Property: $\sqrt{2 \times 3^2 \times 5}$ $\newline$ Apply the product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{2 \times 3^2 \times 5} = \sqrt{3^2} \times \sqrt{2 \times 5}$
Simplify Perfect Square: $\sqrt{90} = \sqrt{3^2} \times \sqrt{2 \times 5}$ $\newline$ Simplify the square root of the perfect square. $\newline$ Square and square root cancel each other out. $\newline$ $\sqrt{3^2} \times \sqrt{2 \times 5} = 3 \times \sqrt{10}$