How do you rationalize the denominator and simplify 1/(sqrt3-2)?

1 Answer
Alan P.
Sep 30, 2015

Multiply the numerator and denominator by bye conjugate of the denominator to get:
color(white)("XXX")-(sqrt(3)+2)

Explanation:

The conjugate of a two-term expression (a+b) is (a-b) and visa versa.
The product of conjugates (a+b)xx(a-b) is a^2-b^2

For the given example, the conjugate of (sqrt(3)-2) is (sqrt(3)+2)

1/(sqrt(3)-2)
color(white)("XXX")=1/(sqrt(3)-2)xx(sqrt(3)+2)/(sqrt(3)+2)

color(white)("XXX")=(sqrt(3)+2)/((sqrt(3)^2-2^2)

color(white)("XXX")=(sqrt(3)+2)/(3-4)

color(white)("XXX")=(sqrt(3)+2)/(-1)

color(white)("XXX")=-(sqrt(3)+2)

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