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How do you rationalize the denominator and simplify #1/(sqrta+sqrtb)#?

1 Answer

Tony B · George C.

Mar 12, 2016

#=(sqrt(a)-sqrt(b))/(a-b)#

Explanation:

Given:#" "1/(sqrt(a)+sqrt(b))#

Known:# (a^2-b^2)=(a+b)(a-b)#

So using the above known information multiply by 1 but in the form of #1=(sqrt(a)-sqrt(b))/(sqrt(a)-sqrt(b))#

So
#=1/(sqrt(a)-sqrt(b)) xx (sqrt(a)-sqrt(b))/(sqrt(a)-sqrt(b))#

#=(sqrt(a)-sqrt(b))/(a-b)#

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