Question

Help? Please? 4/ 5 + √2

Answer 1

What do you want done?

Answer 2

I need to rationalize the denominator. I have no idea what the steps are. I read my text book, but I'm so confused.

Answer 3

Is it \[\frac{4}{5+\sqrt{2}}\]

Answer 4

\[4 \over {5+\sqrt{2}}\] so you multiply both the numerator and denominator by the conjugate of the denominator.
\[5+\sqrt{2}\] conjugate is \[5 - \sqrt{2}\] so you get
\[(5+\sqrt{2})(5-\sqrt{2})\] and as you know \[(a+b)((a-b)=a^2-b^2\]
So the denominator becomes
\[5^2-(\sqrt{2})^2=25-2=23\]
Leaving you with
\[{{4(5-\sqrt{2})} \over 23}={{20-4 \sqrt{2}} \over 23}\]

Answer 5

@op Please do a little better with your notation if this is correct. If you mean the expression that has been the target of this worked exercise, you have not written wat you intended.

4 / 5 + sqrt(2) = \[\frac{4}{5}+\sqrt{2}\]

4 / (5 + sqrt(2)) = \[\frac{4}{5+\sqrt{2}}\]

Always remember your Order of Operations. Use parentheses to clarify meaning.