Question

simplify by rationalizing the denominator
\[\frac a{\sqrt{10}+\sqrt2}\]

Answer 1

you should try to rewrite your question using the equation editor

Answer 2

were is that?

Answer 3

the \(\Sigma\) symbol button that says equation on the lower-left of the reply box

Answer 4

oh ok thank u

Answer 5

a\[\frac{ a }{ \sqrt{10+\sqrt{2}} }\]

Answer 6

I'm guessing you meant\[\frac a{\sqrt{10}+\sqrt2}\]right?

Answer 7

yes

Answer 8

rationalizing means multiplying the numerator and denominator by the conjugate. the conjugate of (a+b) = (a-b)

Answer 9

so multiply by\[\frac{\sqrt{10}-\sqrt2}{\sqrt{10}-\sqrt2}\]

Answer 10

So that would cancel it out?

Answer 11

well it is true that you can cancel the above to 1, but that's not going to do anything, is it? we multiply the numerator and denominator by something divided by itself precisely because it *is* equal to one, and therefor does not change the value of the expression.

Answer 12

so just carry out the multiplication normally... remember what (a+b)(a-b) is....

Answer 13

no

Answer 14

well if you don't remember what (a+b)(a-b) equals just FOIL it out

Answer 15

ok that is right

Answer 16

\[a/\sqrt{20}\]

Answer 17

no, we multiply top and bottom by \(\sqrt{10}-\sqrt2\)
what is that times \(\sqrt{10}+\sqrt2\)

Answer 18

?

Answer 19

for some reason I am getting 10

Answer 20

not quite...
in general, what do you get by FOILing out (a+b)(a-b) ?

Answer 21

you would times both a then b right?

Answer 22

The FOIL method:if you don't remember how to FOIL you should go back a few steps and see what you missed in earlier algebra.