• Oct 30th 2008, 05:05 AM
william
simplify and state restrictions on the variable
a)(4+squareroot2)(5-squareroot8)
b)2squareroot5+squareroot5
c)3squareroot7-5squareroot7
d)squareroot35/squareoot7
• Oct 30th 2008, 05:57 AM
superevilcube
1) I don't know how to make it pretty, so I hope this works: First foil it:
$(4+sqrt(2))(5-sqrt(8))$
$(4)(5) - 4sqrt(8) + 5sqrt(2) - sqrt(2)sqrt(8)$

Now you need to simplify $sqrt(8)$ and $sqrt(8)sqrt(2)$

This is how I do it: Take sqrt(8) and break it into it's factors, so you have:

$sqrt(8)=sqrt(2*4)=sqrt(2)*sqrt(4)=2*sqrt(2)$

Make sense? So if you do that we have:

$20 - 4*2*sqrt(2) + 5sqrt(2) - sqrt(16)$

Now you can just simplify:

$16 - 3sqrt(2)$

2) This one is a cinch:

$2sqrt(5) + sqrt(5) = 3sqrt(5)$

Do you see why?

3) This is the same as 2.

4) You need to break sqrt(35) into it's factors:

$sqrt(35) = sqrt(5*7) = sqrt(5)sqrt(7)$

Now we have:

$sqrt(35)/sqrt(7) = sqrt(5)sqrt(7)/sqrt(7) = sqrt(5)$

The two sqrt(7)s just cancel out.