Question

Rationalize the denominator. The answer should be expressed in simplified form.

Answer 1

\[\frac{ \sqrt{2} }{ \sqrt{11}-\sqrt{5} }\]

Answer 2

\[\frac{ \sqrt{10} }{ 6 }+\frac{ \sqrt{22} }{ 6 }\]
Is that correct?

Answer 3

@iambatman

Answer 4

for question 1, multiply by a conjugate top and bottom.
Also, iambatman is very very smart, but he is offline right now.

Answer 5

In this conjugate is \(\large\color{black}{ \bf \sqrt{11}+\sqrt{5} }\)

Answer 6

How did it become plus?

Answer 7

it didn't \(\large\color{red}{ \bf become }\) plus, I am using a conjugate to rationalize the denominator.

Answer 8

Oooh, I get it now

Answer 9

SO tell me what do you get when you multiply top and bottom times \(\large\color{brown }{ \bf \sqrt{11}+\sqrt{5} }\) ?

Answer 10

\[\sqrt{22} + \sqrt{10}\]
The bottom would just be: 11 & 5

Answer 11

are actually correct, I thought it was another problem... duh, I am so dumb !

And the bottom would be 11-5, b/c

\(\large\color{black}{ \bf (a-b)(a+b)=a^2 }\) \(\large\color{red}{ \bf - }\) \(\large\color{black}{ \bf b^2 }\)

Answer 12

and 11-5 is 6.

Answer 13

So, my answer is correct?

Answer 14

You are NOT dumb, at all lol

Answer 15

Yes, your answer is correct :)

Answer 16

O r can i just put both of the numerators together on top & just have one 6 on the bottom or does it have to be like that?

Answer 17

\(\large\color{black}{ \bf \frac{\Huge \sqrt{10}+\sqrt{22} }{\Huge6} }\) and what you have is the same exact thing, but I think it is a tiny bit better to write them as one fraction.

Answer 18

Ok, thank you!