Simplify. sqrt 490 ______

Find Prime Factors: sqrt(490) 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(490) = sqrt(2 * 5 * 7 * 7)Group and Combine Factors: sqrt(2 * 5 * 7 * 7) Now, group the identical factors. Combine the identical factors by using the exponents. sqrt(2 * 5 * 7 * 7) = sqrt(2 * 5 * 7^2)Apply Product Property: sqrt(2 * 5 * 7^2) Product property of radicals: sqrt(a * b) = sqrt(a) * sqrt(b) sqrt(2 * 5 * 7^2) = sqrt(2) * sqrt(5) * sqrt(7^2)Cancel Perfect Squares: sqrt(490) = sqrt(2) * sqrt(5) * sqrt(7^2) Square and square root cancel each other out for the perfect square factor. sqrt(2) * sqrt(5) * sqrt(7^2) = sqrt(2) * sqrt(5) * 7Combine Remaining Square Roots: sqrt(490) = sqrt(2) * sqrt(5) * 7 Since there are no more perfect square factors, we can combine the remaining square roots. sqrt(2) * sqrt(5) = sqrt(2 * 5) sqrt(490) = sqrt(10) * 7Final Simplified Form: sqrt(490) = 7 * sqrt(10) This is the simplified form of the square root of 490.

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Simplify. $\newline$ $\sqrt{490}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify.

\newline

\sqrt{490}

Find Prime Factors: $\sqrt{490}$ $\newline$ 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. $\newline$ $\sqrt{490} = \sqrt{2 \times 5 \times 7 \times 7}$
Group and Combine Factors: $\sqrt{2 \times 5 \times 7 \times 7}$ Now, group the identical factors. Combine the identical factors by using the exponents. $\sqrt{2 \times 5 \times 7^2}$
Apply Product Property: $\sqrt{2 \times 5 \times 7^2}$ $\newline$ Product property of radicals: $\newline$ $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ $\newline$ $\sqrt{2 \times 5 \times 7^2} = \sqrt{2} \times \sqrt{5} \times \sqrt{7^2}$
Cancel Perfect Squares: $\sqrt{490} = \sqrt{2} \times \sqrt{5} \times \sqrt{7^2}$ $\newline$ Square and square root cancel each other out for the perfect square factor. $\newline$ $\sqrt{2} \times \sqrt{5} \times \sqrt{7^2} = \sqrt{2} \times \sqrt{5} \times 7$
Combine Remaining Square Roots: $\sqrt{490} = \sqrt{2} \times \sqrt{5} \times 7$ Since there are no more perfect square factors, we can combine the remaining square roots. $\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5}$ $\sqrt{490} = \sqrt{10} \times 7$
Final Simplified Form: $\sqrt{490} = 7 \times \sqrt{10}$ $\newline$ This is the simplified form of the square root of $490$ .