Simplify. Assume j is greater than or equal to zero. sqrt 12j^6 ______

Factor and Express: sqrt(12j^6) First, we need to factor the radicand (the number inside the square root) into its prime factors and express the variable j with an exponent that can be simplified. sqrt(12j^6) = sqrt(2 * 2 * 3 * j^6)Group and Simplify: sqrt(2 * 2 * 3 * j^6) Now, group the identical factors and express the variable j with an exponent that can be simplified. sqrt(2 * 2 * 3 * j^6) = sqrt(2^2 * 3 * j^6)Apply Product Property: sqrt(2^2 * 3 * j^6) Apply the product property of radicals to separate the perfect square from the rest. sqrt(2^2 * 3 * j^6) = sqrt(2^2) * sqrt(3) * sqrt(j^6)Simplify Perfect Squares: sqrt(2^2) * sqrt(3) * sqrt(j^6) Simplify the square roots of the perfect squares. sqrt(2^2) * sqrt(3) * sqrt(j^6) = 2 * sqrt(3) * j^3 Since j is greater than or equal to zero, we can take the square root of j^6 as j^3.Combine Constants and Variables: Final Simplification Combine the constants and the simplified variable part. 2 * sqrt(3) * j^3 = 2j^3 * sqrt(3) This is the simplified form of the original expression.

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Simplify. Assume $j$ is greater than or equal to zero. $\newline$ $\sqrt{12j^6}$

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Q. Simplify. Assume

j

is greater than or equal to zero.

\newline

\sqrt{12j^6}

Factor and Express: $\sqrt{12j^6}$ $\newline$ First, we need to factor the radicand (the number inside the square root) into its prime factors and express the variable $j$ with an exponent that can be simplified. $\newline$ $\sqrt{12j^6} = \sqrt{2 \times 2 \times 3 \times j^6}$
Group and Simplify: $\sqrt{2 \times 2 \times 3 \times j^6}$ $\newline$ Now, group the identical factors and express the variable $j$ with an exponent that can be simplified. $\newline$ $\sqrt{2 \times 2 \times 3 \times j^6} = \sqrt{2^2 \times 3 \times j^6}$
Apply Product Property: $\sqrt{2^2 \times 3 \times j^6}$ $\newline$ Apply the product property of radicals to separate the perfect square from the rest. $\newline$ $\sqrt{2^2 \times 3 \times j^6} = \sqrt{2^2} \times \sqrt{3} \times \sqrt{j^6}$
Simplify Perfect Squares: $\sqrt{2^2} \times \sqrt{3} \times \sqrt{j^6}$ $\newline$ Simplify the square roots of the perfect squares. $\newline$ $\sqrt{2^2} \times \sqrt{3} \times \sqrt{j^6} = 2 \times \sqrt{3} \times j^3$ $\newline$ Since $j$ is greater than or equal to zero, we can take the square root of $j^6$ as $j^3$ .
Combine Constants and Variables: Final Simplification $\newline$ Combine the constants and the simplified variable part. $\newline$ $2 \cdot \sqrt{3} \cdot j^3 = 2j^3 \cdot \sqrt{3}$ $\newline$ This is the simplified form of the original expression.