How do you simplify: the square root of 24x times the square root of 6x?

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How do you simplify: the square root of 24x times the square root of 6x?

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Answer 1 · 2015-07-28T00:12:20

Your problem stated:

$\sqrt{24 x} \sqrt{6 x}$ $sqrt(24x)sqrt(6x)$

which already implies the positive domain of $x$ $x$ .

You can combine the square roots to get:

$= \sqrt{24 x \cdot 6 x}$ $= sqrt(24x*6x)$

Multiply stuff in the square root:
$= \sqrt{24 \cdot 6 \cdot x^{2}}$ $= sqrt(24*6*x^2)$

Pull $x^{2}$ $x^2$ out by reversing the first step, basically, and evaluating the result:
$= \sqrt{24 \cdot 6} x$ $= sqrt(24*6)x$
(this is OK without absolute values because the original problem had only positive $\sqrt{x}$ $sqrtx$ .)

$= \sqrt{144} x$ $=sqrt(144)x$

$= 12 x$ $= color(blue)(12x)$

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How do you simplify: the square root of 24x times the square root of 6x?

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