How do you rationalize the denominator and simplify #6/(sqrt4-sqrt14)#?

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Answer 1 · 2018-03-27T14:02:17

#6/(sqrt4-sqrt14)=-3/5(sqrt4+sqrt14)#

To rationalise a surd, we multiply the denominator and numerator by its conjugate.

The conjugate of #sqrta+sqrtb# is #sqrta-sqrtb#.

So,

#6/(sqrt4-sqrt14)#

#=(6(sqrt4+sqrt14))/((sqrt4-sqrt14)(sqrt4+sqrt14))#

#=(6(sqrt4+sqrt14))/(4-14)#

#=6/-10(sqrt4+sqrt14)#

#=-3/5(sqrt4+sqrt14)#