Question

rationalizing the denominator?


https://media.glynlyon.com/a_matalg02_2011/6/test6p15.gif

Answer 1

you need to multiply but a term

\[\frac{3\sqrt{3}+2\sqrt{2}}{3\sqrt{3}+2\sqrt{2}}\]

this is a same as multiplying by 1... just written in a different form.

so the problem becomes

\[\frac{(2\sqrt{3}+5\sqrt{2})\times(3\sqrt{3}+2\sqrt{2})}{(3\sqrt{3}-2\sqrt{2})\times(3\sqrt{3}+2\sqrt{2)}}\]

the denominator is the difference of 2 squares and will result in a rational number in the denominator...

the denominator simplifies to 19, i'll leave you to do the numerator