Simplify. sqrt 245 ______

Find Prime Factors: sqrt(245) 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(245) = sqrt(5 * 7 * 7)Group and Combine Factors: sqrt(5 * 7 * 7) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(5 * 7 * 7) = sqrt(5 * 7^2)Apply Product Property: sqrt(5 * 7^2) Apply the product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(5 * 7^2) = sqrt(5) * sqrt(7^2)Simplify Perfect Square: sqrt(245) = sqrt(5) * sqrt(7^2) Simplify the square root of the perfect square. Square and square root cancel each other out. sqrt(5) * sqrt(7^2) = sqrt(5) * 7Final Simplification: sqrt(245) = sqrt(5) * 7 The simplest form of sqrt(245) is: 7 * sqrt(5) = 7sqrt(5)

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Simplify. $\newline$ $\sqrt{245}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{245}

Find Prime Factors: $\sqrt{245}$ $\newline$ 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. $\newline$ $\sqrt{245} = \sqrt{5 \times 7 \times 7}$
Group and Combine Factors: $\sqrt{5 \times 7 \times 7}$ $\newline$ Now, group the identical factors. $\newline$ Combine the identical factors by using the exponents. $\newline$ $\sqrt{5 \times 7^2}$
Apply Product Property: $\sqrt{5 \times 7^2}$ $\newline$ Apply the product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{5 \times 7^2} = \sqrt{5} \times \sqrt{7^2}$
Simplify Perfect Square: $\sqrt{245} = \sqrt{5} \times \sqrt{7^2}$ $\newline$ Simplify the square root of the perfect square. $\newline$ Square and square root cancel each other out. $\newline$ $\sqrt{5} \times \sqrt{7^2} = \sqrt{5} \times 7$
Final Simplification: $\sqrt{245} = \sqrt{5} \times 7$ $\newline$ The simplest form of $\sqrt{245}$ is: $\newline$ $7 \times \sqrt{5}$ $\newline$ $= 7\sqrt{5}$