CoffeeEyes 2 years ago Help? Please? 4/ 5 + √2

1. PhoenixFire

What do you want done?

2. CoffeeEyes

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

3. tkhunny

Is it $\frac{4}{5+\sqrt{2}}$

4. PhoenixFire

$4 \over {5+\sqrt{2}}$ 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 ${{4(5-\sqrt{2})} \over 23}={{20-4 \sqrt{2}} \over 23}$

5. tkhunny

@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.