How do you rationalize the denominator and simplify 3/(2-sqrt2)?

1 Answer
Shwetank Mauria
Jun 23, 2016

3/(2-sqrt2)=3+3/2sqrt2

Explanation:

To rationalize the denominator and simplify 3/(2-sqrt2), we should multiply numerator and denominator by the conjugate of denominator. As denominator is 2-sqrt2, its conjugate is 2+sqrt2.

3/(2-sqrt2)=(3xx(2+sqrt2))/((2+sqrt2)xx(2-sqrt2))

= (6+3sqrt2)/(2^2-2)

= (6+3sqrt2)/(4-2)

= (6+3sqrt2)/2=3+3/2sqrt2

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