Question

I need some help rationalizing these denominators. Can anyone help?

Answer 1

\[\frac{ 4 }{ 3-3\sqrt{2} }\]

Answer 2

Multiply by the conjugate of the denominator \(3+\sqrt2\) divided by itself
\[\frac{ 4 }{ 3-3\sqrt{2} }\times \frac{ 3+3\sqrt2 }{ 3+3\sqrt2}\]

Answer 3

wouldn't we multiply the top and bottom by \[-3\sqrt{3}\]

Answer 4

no. you need to use the conjugate because it gives a difference of squares in the denominator and the radicals will cancel

Answer 5

okay so would we end up with \[\frac{ 12\sqrt{3} }{ 3 }\] ?

Answer 6

no. It looks like you multiplied by something with √3.