Question

6-√8 divide √2-1

this is rationalising surd question I did it and my answer is not right so could someone do this to me and show your working out
thanks

Answer 1

4
`√(2)` +2

Explanation:

`(6-√(8))/(√(2)-1)`

=
`(6-√(8))/(√(2)-1)` ×
`(√(2)+1)/(√(2)+1)`

=
`((6-√(8))(√(2)+1))/(2-1)`

=6
`√(2)` + 6 -
`√(8)√(2)` -
`√(8)`

=6
`√(2)` + 6 - 4 -
`√(8)`

=6
`√(2)` + 2 -
`√(8)`

=6
`√(2)` + 2 - 2

=4
`√(2)` +2

for
`√(8)` = 2
`√(2)` ,

`√(8)` =
`√(2*2*2)`

= (
`√(2)`)^2 ×
`√(2)`

=2 ×
`√(2)`