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Simplify.
Remove all perfect squares from inside the square root.

sqrt(112a^(6))=

Simplify. $\newline$ Remove all perfect squares from inside the square root. $\newline$ $\sqrt{112a^{6}}$

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Simplify radical expressions with variables

Full solution

Q. Simplify.

\newline

Remove all perfect squares from inside the square root.

\newline

\sqrt{112a^{6}}

Identify Perfect Square Factors: Identify the perfect square factors of the number under the square root. $112$ can be factored into $56 \times 2$ , and $56$ can be further factored into $8 \times 7$ , where $8$ is a perfect square (since $8 = 2^2 \times 2^2$ ). For the variable part, $a^{6}$ is a perfect square since $(a^3)^2 = a^{6}$ .
Separate Perfect Square Factors: Rewrite the square root of the number by separating the perfect square factors. $\sqrt{112a^{6}} = \sqrt{8 \times 14 \times a^{6}} = \sqrt{8} \times \sqrt{14} \times \sqrt{a^{6}}$
Simplify Square Roots: Simplify the square roots of the perfect squares. $\sqrt{8} = 2 \times 2 = 4$ and $\sqrt{a^{6}} = a^{3}$ because $(a^{3})^2 = a^{6}$ .
Combine Simplified Roots: Combine the simplified square roots with the part that cannot be simplified. $\sqrt{112a^{6}} = 4 \times \sqrt{14} \times a^{3}$
Write Final Expression: Write the final simplified expression. $\newline$ The final simplified expression is $4a^{3} \times \sqrt{14}$ .

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