If k>0 , then \frac{1}{\sqrt{5k} + \sqrt{k}} =... | Free GMAT Practice Question | GMAT Panda

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GMAT Quant — Quant (Roots)

If k > 0, then \frac{1}{5 k + k} =

Explanation	Calculations	Help
$We multiply the fraction by the expression over itself to clear roots from the denominator.$	$\frac{1}{5 k + k} \times \frac{5 k - k}{5 k - k}$	Theory & Tactics Method Card FDPR0-C Click to view full details
$We use the difference of squares to simplify the denominator.$	$\frac{5 k - k}{5 k - k} = \frac{5 k - k}{4 k}$	Theory & Tactics Method Card EXP4-B Click to view full details
$We factor out k from the numerator.$	$\frac{k ( 5 - 1 )}{4 k}$
$We write k as k \times k in the denominator and cancel a common factor of k .$	$\frac{k ( 5 - 1 )}{4 k k} = \frac{( 5 - 1 ) k}{4 k k} = \frac{5 - 1}{4 k}$	Theory & Tactics Method Card FDPR2-A Click to view full details

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D

GMAT Quant — Quant (Roots)

If k > 0, then \frac{1}{5 k + k} =

Explanation	Calculations	Help
$We multiply the fraction by the expression over itself to clear roots from the denominator.$	$\frac{1}{5 k + k} \times \frac{5 k - k}{5 k - k}$	Theory & Tactics Method Card FDPR0-C Click to view full details
$We use the difference of squares to simplify the denominator.$	$\frac{5 k - k}{5 k - k} = \frac{5 k - k}{4 k}$	Theory & Tactics Method Card EXP4-B Click to view full details
$We factor out k from the numerator.$	$\frac{k ( 5 - 1 )}{4 k}$
$We write k as k \times k in the denominator and cancel a common factor of k .$	$\frac{k ( 5 - 1 )}{4 k k} = \frac{( 5 - 1 ) k}{4 k k} = \frac{5 - 1}{4 k}$	Theory & Tactics Method Card FDPR2-A Click to view full details

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D