Multiply. Write your answer in simplest form. sqrt26*sqrt455

Find Prime Factorization: Find the prime factorization of sqrt(26) and sqrt(455). The prime factorization of 26 is 2 * 13, and the prime factorization of 455 is 5 * 7 * 13.Combine Square Roots: Combine the square roots using the multiplication property: sqrt(26) * sqrt(455) = sqrt(26 * 455).Multiply Inside Square Root: Multiply the numbers inside the square root: sqrt(26 * 455) = sqrt(11830).Factor to Find Perfect Squares: Factor 11830 to find perfect squares: 11830 = 2 * 5 * 7 * 13 * 13.Group Perfect Square Factors: Group the perfect square factors: sqrt(2 * 5 * 7 * 13 * 13) = sqrt(2 * 5 * 7 * 13^2).Pull Out Perfect Square Factor: Pull out the perfect square factor: sqrt(2 * 5 * 7 * 13^2) = 13 * sqrt(2 * 5 * 7).Simplify the Expression: Simplify the expression: 13 * sqrt(2 * 5 * 7) = 13 * sqrt(70).

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Multiply. Write your answer in simplest form. $\newline$ $\sqrt{26}\cdot\sqrt{455}$

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Q. Multiply. Write your answer in simplest form.

\newline

\sqrt{26}\cdot\sqrt{455}

Find Prime Factorization: Find the prime factorization of $\sqrt{26}$ and $\sqrt{455}$ . The prime factorization of $26$ is $2 \times 13$ , and the prime factorization of $455$ is $5 \times 7 \times 13$ .
Combine Square Roots: Combine the square roots using the multiplication property: $\sqrt{26} \times \sqrt{455} = \sqrt{26 \times 455}$ .
Multiply Inside Square Root: Multiply the numbers inside the square root: $\sqrt{26 \times 455} = \sqrt{11830}$ .
Factor to Find Perfect Squares: Factor $11830$ to find perfect squares: $11830 = 2 \times 5 \times 7 \times 13 \times 13$ .
Group Perfect Square Factors: Group the perfect square factors: $\sqrt{2 \times 5 \times 7 \times 13 \times 13} = \sqrt{2 \times 5 \times 7 \times 13^2}$ .
Pull Out Perfect Square Factor: Pull out the perfect square factor: $\sqrt{2 \times 5 \times 7 \times 13^2} = 13 \times \sqrt{2 \times 5 \times 7}$ .
Simplify the Expression: Simplify the expression: $13 \times \sqrt{2 \times 5 \times 7} = 13 \times \sqrt{70}.$