What is the square root of (x^6)/27?

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What is the square root of (x^6)/27?

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Answer 1 · 2015-07-18T16:52:20

$\sqrt{\frac{x^{6}}{27}} = \frac{\sqrt{3}}{9} ∣ ∣ x^{3} ∣ ∣$ $sqrt((x^6)/27) = sqrt(3)/9 abs(x^3)$

Explanation:

If $a, b \geq 0$ $a, b >= 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$ $sqrt(ab) = sqrt(a)sqrt(b)$ and $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(a/b) = sqrt(a)/sqrt(b)$

$\sqrt{\frac{x^{6}}{27}} = \sqrt{\frac{3 x^{6}}{81}} = \frac{\sqrt{x^{6}} \sqrt{3}}{\sqrt{81}} = \frac{∣ ∣ x^{3} ∣ ∣ \sqrt{3}}{9} = \frac{\sqrt{3}}{9} ∣ ∣ x^{3} ∣ ∣$ $sqrt((x^6)/27) = sqrt((3x^6)/81) = (sqrt(x^6)sqrt(3))/sqrt(81) = (abs(x^3)sqrt(3))/9 = sqrt(3)/9 abs(x^3)$

Note $∣ ∣ x^{3} ∣ ∣$ $abs(x^3)$ , not $x^{3}$ $x^3$ .

If $x < 0$ $x < 0$ then $x^{3} < 0$ $x^3 < 0$ , but $\sqrt{x^{6}} > 0$ $sqrt(x^6) > 0$ since $\sqrt{}$ $sqrt$ denotes the positive square root.

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What is the square root of (x^6)/27?

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