simplify and state restrictions on the variable

a)(4+squareroot2)(5-squareroot8)

b)2squareroot5+squareroot5

c)3squareroot7-5squareroot7

d)squareroot35/squareoot7

Printable View

- Oct 30th 2008, 05:05 AMwilliamevaluating radicals
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 AMsuperevilcube
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.