Find Prime Factors: sqrt(50) 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(50) = sqrt(2 * 5 * 5)Group and Combine Factors: sqrt(2 * 5 * 5) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(2 * 5 * 5) = sqrt(2 * 5^2)Apply Product Property: sqrt(2 * 5^2) Product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(2 * 5^2) = sqrt(2) * sqrt(5^2)Simplify and Final Answer: sqrt(50) = sqrt(2) * sqrt(5^2) What is the simplest form of sqrt(50)? Square and square root cancel each other out. sqrt(2) * sqrt(5^2) = sqrt(2) * 5 = 5sqrt(2)

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Simplify. $\newline$ $\sqrt{50}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{50}

Find Prime Factors: $\sqrt{50}$ $\newline$ 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. $\newline$ $\sqrt{50} = \sqrt{2 \times 5 \times 5}$
Group and Combine Factors: $\sqrt{2 \times 5 \times 5}$ $\newline$ Now, group the identical factors. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{2 \times 5^2}$
Apply Product Property: $\sqrt{2 \times 5^2}$ $\newline$ Product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{2 \times 5^2} = \sqrt{2} \times \sqrt{5^2}$
Simplify and Final Answer: $\sqrt{50} = \sqrt{2} \times \sqrt{5^2}$ $\newline$ What is the simplest form of $\sqrt{50}$ ? $\newline$ Square and square root cancel each other out. $\newline$ $\sqrt{2} \times \sqrt{5^2}$ $\newline$ = $\sqrt{2} \times 5$ $\newline$ = $5\sqrt{2}$