Simplify. Assume b is greater than or equal to zero. sqrt 75b^3 ______

Factorize Perfect Squares: Factorize 75b^3 to find perfect squares. The prime factorization of 75 is 3 * 5 * 5, and b^3 is b * b * b. So, 75b^3 can be written as 3 * 5^2 * b^2 * b.Group Perfect Squares: Group the perfect squares under the square root. We have sqrt(75b^3) = sqrt(3 * 5^2 * b^2 * b). The perfect squares are 5^2 and b^2, which can be taken out of the square root.Simplify Square Root: Simplify the square root by taking out the perfect squares. Taking the square root of the perfect squares gives us 5b, and we are left with sqrt(3b) inside the radical. So, sqrt(75b^3) = 5b * sqrt(3b).

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Simplify. Assume $b$ is greater than or equal to zero. $\newline$ $\sqrt{75b^3}$

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Algebra 1

Simplify radical expressions with variables

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Q. Simplify. Assume

b

is greater than or equal to zero.

\newline

\sqrt{75b^3}

Factorize Perfect Squares: Factorize $75b^3$ to find perfect squares. $\newline$ The prime factorization of $75$ is $3 \times 5 \times 5$ , and $b^3$ is $b \times b \times b$ . So, $75b^3$ can be written as $3 \times 5^2 \times b^2 \times b$ .
Group Perfect Squares: Group the perfect squares under the square root. $\newline$ We have $\sqrt{75b^3} = \sqrt{3 \times 5^2 \times b^2 \times b}$ . $\newline$ The perfect squares are $5^2$ and $b^2$ , which can be taken out of the square root.
Simplify Square Root: Simplify the square root by taking out the perfect squares. Taking the square root of the perfect squares gives us $5b$ , and we are left with $\sqrt{3b}$ inside the radical. So, $\sqrt{75b^3} = 5b \times \sqrt{3b}$ .