How do you simplify $\sqrt{x^{6} \cdot y^{6}}$ $sqrt(x^6*y^6)$ ?

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How do you simplify $\sqrt{x^{6} \cdot y^{6}}$ $sqrt(x^6*y^6)$ ?

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Answer 1 · 2015-07-23T02:14:44

First rewrite, as $x^{6} = {(x^{3})}^{2} and y^{6} = {(y^{3})}^{2}$ $x^6=(x^3)^2and y^6=(y^3)^2$

Explanation:

$= \sqrt{{(x^{3})}^{2} \cdot {(y^{3})}^{2}} = \sqrt{{(x^{3})}^{2}} \cdot \sqrt{{(y^{3})}^{2}})$ $=sqrt((x^3)^2*(y^3)^2)=sqrt((x^3)^2)*sqrt((y^3)^2))$

$= x^{3} \cdot y^{3} = x^{3} y^{3}$ $=x^3*y^3=x^3y^3$

Answer 2 · 2015-07-31T06:14:27

$\sqrt{x^{6} \cdot y^{6}} = ∣ ∣ x^{3} y^{3} ∣ ∣$ $sqrt(x^6*y^6) = abs(x^3y^3)$

Explanation:

$\sqrt{x^{6} \cdot y^{6}} = \sqrt{{(x y)}^{6}} = \sqrt{{({(x y)}^{3})}^{2}} = ∣ ∣ {(x y)}^{3} ∣ ∣ = ∣ ∣ x^{3} y^{3} ∣ ∣$ $sqrt(x^6*y^6) = sqrt((xy)^6) = sqrt(((xy)^3)^2) = abs((xy)^3) = abs(x^3y^3)$

using $\sqrt{a^{2}} = | a |$ $sqrt(a^2) = abs(a)$ for all $a in RR$ .

Note especially that we need the absolute value to cover the case where $a < 0$ , since $sqrt$ denotes the positive square root.

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How do you simplify $\sqrt{x^{6} \cdot y^{6}}$ $sqrt(x^6*y^6)$ ?

2 Answers

Explanation:

Explanation:

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How do you simplify $\sqrt{x^{6} \cdot y^{6}}$ $sqrt(x^6*y^6)$ ?