Simplify. sqrt 8/9 ______

Apply Quotient Rule of Radicals: Apply the quotient rule of radicals to sqrt(8/9). sqrt(8/9) = sqrt(8) / sqrt(9)Evaluate sqrt(8): Evaluate sqrt(8). Find the prime factorization of 8 and try to make identical pairs of factors. sqrt(8) = sqrt(2 * 2 * 2) = sqrt(2^2 * 2) = 2 * sqrt(2)Evaluate sqrt(9): Now, let's evaluate sqrt(9). sqrt(9) = sqrt(3 * 3) = 3Combine Results: Combine the results from the previous steps. sqrt(8/9) = (2 * sqrt(2)) / 3

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Simplify. $\newline$ $\sqrt{\frac{8}{9}}$

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Algebra 2

Simplify radical expressions involving fractions

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Q. Simplify.

\newline

\sqrt{\frac{8}{9}}

Apply Quotient Rule of Radicals: Apply the quotient rule of radicals to $\sqrt{\frac{8}{9}}$ . $\sqrt{\frac{8}{9}} = \frac{\sqrt{8}}{\sqrt{9}}$
Evaluate $\sqrt{8}$ : Evaluate $\sqrt{8}$ . Find the prime factorization of $8$ and try to make identical pairs of factors. $\sqrt{8} = \sqrt{2 \times 2 \times 2}$ = $\sqrt{2^2 \times 2}$ = $2 \times \sqrt{2}$
Evaluate $\sqrt{9}$ : Now, let's evaluate $\sqrt{9}$ . $\newline$ $\sqrt{9} = \sqrt{3 \times 3}$ $\newline$ $= 3$
Combine Results: Combine the results from the previous steps. $\sqrt{\frac{8}{9}} = \frac{2 \cdot \sqrt{2}}{3}$