• 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:
\$\displaystyle (4+sqrt(2))(5-sqrt(8))\$
\$\displaystyle (4)(5) - 4sqrt(8) + 5sqrt(2) - sqrt(2)sqrt(8)\$

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

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

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

Make sense? So if you do that we have:

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

Now you can just simplify:

\$\displaystyle 16 - 3sqrt(2)\$

2) This one is a cinch:

\$\displaystyle 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:

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

Now we have:

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

The two sqrt(7)s just cancel out.