How do you simplify $\sqrt{24 x^{3} y z}$ $sqrt(24x^3yz)$ ?

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How do you simplify $\sqrt{24 x^{3} y z}$ $sqrt(24x^3yz)$ ?

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Answer 1 · 2015-09-23T16:24:43

$= 2 x \sqrt{6 x y z}$ $=2x sqrt(6 x y z)$

Explanation:

Fully factorising all terms (to assist clarity)

$\sqrt{24 x^{3} y z} = \sqrt{2 \cdot 2 \cdot 2 \cdot 3 \cdot x \cdot x \cdot x \cdot y \cdot z}$ $sqrt(24 x^3 y z) = sqrt(2 * 2 * 2 * 3 * x * x * x * y *z)$

Collecting terms that can be expressed as squares

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

Taking squared terms outside the square root sign (taking their square roots whilst doing so)

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

Reforming the compound number from the residua for neatness

$= 2 x \sqrt{6 x y z}$ $= 2x sqrt(6 x y z)$

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How do you simplify $\sqrt{24 x^{3} y z}$ $sqrt(24x^3yz)$ ?

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How do you simplify $\sqrt{24 x^{3} y z}$ $sqrt(24x^3yz)$ ?