Question

How do you simplify `(2sqrt 8 + 7sqrt8)/(1 - sqrt2)`?

Answer 1

We can add the terms in the numerator and then rationalize:
`(9sqrt(8))/(1-sqrt(2))*(1+sqrt(2))/(1+sqrt(2))=`
`=(9sqrt(8)(1+sqrt(2)))/(1-2)=`
`=-9sqrt(4*2)(1+sqrt(2))=`
`=-18sqrt(2)(1+sqrt(2))`

Answer 2

1. Simplify the numerator.
2. Multiply the numerator and denominator by the conjugate of the denominator.
3. Simplify a bit more.

Step 1
`2sqrt(8)+7sqrt(8)`
`= 9sqrt(8)`
`=9sqrt(2^*2)`
`=18sqrt(2)`

Step2
`(18sqrt(2))/(1-sqrt(2)) * (1+sqrt(2))/(1+sqrt(2))`

`= (18sqrt(2)+36)/(1-(sqrt(2)^2)`

Step 3
`= - (36+18sqrt(2))`