Question

rationalize sqr(2)/3sqr(3)-sqr(2)

Answer 1

multiply by 1 in the form

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

this creates the difference on 2 squares in the denominator and will leave a rational number..

you need to evaluate

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

Answer 2

\[3\sqrt{3} \times 3\sqrt{3} = (3\times3)(\sqrt{3}\times \sqrt{3}) = 9 \times3 = 27\]

\[\sqrt{4} = 2\]

so you denominator should be 27 - 2 = 25