Question

Simplify this:

4√3
----------
√5 - 3√2

= 4√3 x √5 + 3√2
------ ----------
√5 - 3 √2 √5 + 3 √2

Basically I am not sure why there is a positive in the second fraction. Shouldn't the denominator be √5 - 3 √2 for both fractions? Thanks.

Answer 1

\[\frac{4\sqrt{3}}{\sqrt{5}-3\sqrt{2}}\times\frac{\sqrt{5}+3\sqrt{2}}{\sqrt{5}+3\sqrt{2}}=\frac{4\sqrt{15}+12\sqrt{6}}{5-18}=\frac{4\sqrt{15}+12\sqrt{6}}{-13}\]

Answer 2

The denominator is correct because you multiply by the conjugate to eliminate the radical from the denominator.

Answer 3

In order to get rid of sqrt under denominator, apply (a -b) (a +b) = a^2 - b^2:

4√3 /( √5 + 3√2) = [ 4√3 ( √5 + 3√2) ] /[ 5 - 18 ] = - ( 4√15 + 12√6 ) / 13

Answer 4

Just attempt to make it more presentable:
= [ 4√3 ( √5 + 3√2) ] /[ 5 - 18 ]
= - ( 4√15 + 12√6 ) / 13