How do you simplify $\sqrt{150 x^{2} y}$ $sqrt(150x^2y)$ ?

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How do you simplify $\sqrt{150 x^{2} y}$ $sqrt(150x^2y)$ ?

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Answer 1 · 2016-01-19T19:54:59

$\sqrt{150 x^{2} y} = 5 | x | \sqrt{6 y}$ $sqrt(150x^2y) = 5abs(x)sqrt(6y)$

Explanation:

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

Note also that $\sqrt{x^{2}} = | x |$ $sqrt(x^2) = abs(x)$ for any Real number $x$ $x$

So:

$\sqrt{150 x^{2} y} = \sqrt{25 \cdot 6 \cdot x^{2} \cdot y} = \sqrt{5^{2}} \cdot \sqrt{6 x^{2} y} = 5 \sqrt{6 x^{2} y}$ $sqrt(150x^2y) = sqrt(25*6*x^2*y)=sqrt(5^2)*sqrt(6x^2y) = 5sqrt(6x^2y)$

$= 5 \sqrt{x^{2}} \sqrt{6 y} = 5 | x | \sqrt{6 y}$ $= 5sqrt(x^2)sqrt(6y) = 5abs(x)sqrt(6y)$

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How do you simplify $\sqrt{150 x^{2} y}$ $sqrt(150x^2y)$ ?

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