Rationalise the fraction : 5/(3-sqrt(2))

To rationalise a fraction we have to eliminate the surds in the denominator. We know we can multiply the top and the bottom of a fraction by the same thing, as this is equivalent to multiplying by 1. Notice that(3-sqrt(2))(3+sqrt(2))=9-3sqrt(2)+3sqrt(2)-2=9-2=7Then we can multiply the fraction by (3+sqrt(2))/(3+sqrt(2)) to eliminate the surd in the denominator.5/(3-sqrt(2)) = 5/(3-sqrt(2)) x 1 = 5/(3-sqrt(2)) x (3+sqrt(2))/(3+sqrt(2)) = 5(3+sqrt(2))/(3-sqrt(2))(3+sqrt(2)) = 5(3+sqrt(2)/7