Rationalize the denominator

Question

Rationalize the denominator of the following problems.

1) 4/3-√11

2)3/³√3

Answer 1

I am assuming that #1 is 4/(3-√11). Make sure to add the parenthesis!

 

First thing you want to do is multiply the top and bottom by 3+√11.

 

[4(3+√11)] / [(3-√11)(3+√11)]

 

before we proceed, lets figure out the denominator:

 

9+3√11-3√11-11

 

as you can see the 3√11's will cancel out giving you

 

9-11=-2

 

Now we can figure the rest out:

 

[4(3+√11)] / -2

 

you can simplify the top and bottom with the 4 and -2 giving you:

 

-2(3+√11)

 

Now for #2.

 

3/³√3 

 

Again multiply both top and bottom by ³√3 giving you:

 

3³√3 / 3

 

we can simplify this by canceling the 3's giving you:

 

³√3.

 

Hope this helps!