Simplify. Assume g is greater than or equal to zero. sqrt 12g^4 ______

Factor and Identify Perfect Squares: sqrt(12g^4) First, we need to factor the radicand (the number inside the square root) into its prime factors and identify perfect squares. sqrt(12g^4) = sqrt(4 * 3 * g^4)Recognize Perfect Squares: sqrt(4 * 3 * g^4) Now, we recognize that 4 is a perfect square and that g^4 is also a perfect square since any even power of a number is a perfect square. sqrt(4 * 3 * g^4) = sqrt(4) * sqrt(3) * sqrt(g^4)Simplify Square Roots: sqrt(4) * sqrt(3) * sqrt(g^4) We can now simplify the square roots of the perfect squares. sqrt(4) * sqrt(3) * sqrt(g^4) = 2 * sqrt(3) * g^2Final Simplification: 2 * sqrt(3) * g^2 Since g is greater than or equal to zero, we can simplify without worrying about the absolute value of g. The simplified form is: 2g^2 * sqrt(3)

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Simplify. Assume $g$ is greater than or equal to zero. $\newline$ $\sqrt{12g^4}$

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Algebra 1

Simplify radical expressions: mixed review

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Q. Simplify. Assume

g

is greater than or equal to zero.

\newline

\sqrt{12g^4}

Factor and Identify Perfect Squares: $\sqrt{12g^4}$ $\newline$ First, we need to factor the radicand (the number inside the square root) into its prime factors and identify perfect squares. $\newline$ $\sqrt{12g^4} = \sqrt{4 \times 3 \times g^4}$
Recognize Perfect Squares: $\sqrt{4 \times 3 \times g^4}$ $\newline$ Now, we recognize that $4$ is a perfect square and that $g^4$ is also a perfect square since any even power of a number is a perfect square. $\newline$ $\sqrt{4 \times 3 \times g^4} = \sqrt{4} \times \sqrt{3} \times \sqrt{g^4}$
Simplify Square Roots: $\sqrt{4} \times \sqrt{3} \times \sqrt{g^4}$ $\newline$ We can now simplify the square roots of the perfect squares. $\newline$ $\sqrt{4} \times \sqrt{3} \times \sqrt{g^4} = 2 \times \sqrt{3} \times g^2$
Final Simplification: $2 \cdot \sqrt{3} \cdot g^2$ $\newline$ Since $g$ is greater than or equal to zero, we can simplify without worrying about the absolute value of $g$ . $\newline$ The simplified form is: $\newline$ $2g^2 \cdot \sqrt{3}$