Rationalize the denominator?

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1 Answer
VNVDVI
Feb 21, 2018

Multiply by the conjugate of the denominator over the conjugate of the denominator, and you'll get #((35-8sqrt(19))/3)# .

Explanation:

Multiply by the conjugate of the denominator over the conjugate of the denominator. This is the same as multiplying by #1#, so doing this will give you an expression equal to what you originally had while removing the square root from your denominator (rationalizing).

The conjugate of the denominator is #sqrt(19)-4#. For any term #(a+b)#, the conjugate is #(a-b)#. For any term #(a-b)#, the conjugate is #(a+b)#.

#((sqrt(19)-4)/(sqrt(19)+4)) * (sqrt(19)-4)/(sqrt(19)-4)#

#(sqrt(19)^2-8sqrt(19)+16)/(sqrt(19)^2-16)#

#(19-8sqrt(19)+16)/(19-16)#

#((35-8sqrt(19))/3)#

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