How do you rationalize the denominator and simplify $4 \sqrt{\frac{7}{2 z^{2}}}$ $4sqrt(7/(2z^2))$ ?

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How do you rationalize the denominator and simplify $4 \sqrt{\frac{7}{2 z^{2}}}$ $4sqrt(7/(2z^2))$ ?

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Answer 1 · 2016-07-31T05:30:33

$4 \sqrt{\frac{7}{2 z^{2}}} = \frac{2 \sqrt{14}}{z}$ $color(blue)(4sqrt(7/(2z^2))=(2sqrt(14))/z)$

$\sqrt[4]{\frac{7}{2 z^{2}}} = \frac{\sqrt[4]{56 z^{2}}}{2 z}$ $color(red)(root4(7/(2z^2))=root4(56z^2)/(2z))$

Explanation:

If the given is to simplify $4 \sqrt{\frac{7}{2 z^{2}}}$ $4sqrt(7/(2z^2)$

The solution:

$4 \sqrt{\frac{7}{2 z^{2}}} = 4 \sqrt{\frac{7}{2 z^{2}} \cdot \frac{2}{2}} = 4 \sqrt{\frac{14}{4 z^{2}}} = \frac{4 \sqrt{14}}{2 z} = \frac{2 \sqrt{14}}{z}$ $4sqrt(7/(2z^2))=4sqrt(7/(2z^2)*2/2)=4sqrt(14/(4z^2))=(4sqrt(14))/(2z)=(2sqrt(14))/z$

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If the given is to simplify $\sqrt[4]{\frac{7}{2 z^{2}}}$ $root4(7/(2z^2))$

The solution:

$\sqrt[4]{\frac{7}{2 z^{2}}} = \sqrt[4]{\frac{7}{2 z^{2}} \cdot (\frac{8 z^{2}}{8 z^{2}})} = \sqrt[4]{\frac{56 z^{2}}{16 z^{4}}} = \frac{\sqrt[4]{56 z^{2}}}{2 z}$ $root4(7/(2z^2))=root4(7/(2z^2)*((8z^2)/(8z^2)))=root4((56z^2)/(16z^4))=root4(56z^2)/(2z)$

God bless....I hope the explanation is useful.

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How do you rationalize the denominator and simplify $4 \sqrt{\frac{7}{2 z^{2}}}$ $4sqrt(7/(2z^2))$ ?

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