How do you simplify $\sqrt{27 x^{4}}$ $sqrt(27x^4 )$ ?

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How do you simplify $\sqrt{27 x^{4}}$ $sqrt(27x^4 )$ ?

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Answer 1 · 2015-10-05T15:34:15

$3 \sqrt{3} x^{2}$ $3sqrt(3)x^2$

Explanation:

First, note that $\sqrt{27 x^{4}} = \sqrt{27} \cdot \sqrt{x^{4}}$ $sqrt(27x^4)=sqrt(27)*sqrt(x^4)$ . Next, since $27 = 9 \cdot 3 = 3^{2} \cdot 3$ $27=9*3=3^2*3$ , we can say $\sqrt{27} = \sqrt{9 \cdot 3} = \sqrt{9} \cdot \sqrt{3} = 3 \cdot \sqrt{3}$ $sqrt(27)=sqrt(9*3)=sqrt(9)*sqrt(3)=3*sqrt(3)$ .

Also, $\sqrt{x^{4}} = \sqrt{{(x^{2})}^{2}} = x^{2}$ $sqrt(x^4)=sqrt((x^2)^2)=x^2$ (in general, $\sqrt{y^{2}} = | y |$ $sqrt(y^2)=|y|$ , but if $y = x^{2}$ $y=x^2$ , then $y \geq 0$ $y\geq 0$ anyway so we can get rid of the absolute value sign).

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How do you simplify $\sqrt{27 x^{4}}$ $sqrt(27x^4 )$ ?

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How do you simplify $\sqrt{27 x^{4}}$ $sqrt(27x^4 )$ ?