Question

6. √(5+2√6)

7. √(4+2√3)

8. √(4-2√3)

9. √(11-2√30)

10. √(21-4√17)

Answer 1

`sqrt{5+2sqrt6}`

`=sqrt{3+2sqrt3sqrt2+2}`

`=sqrt{(sqrt3+sqrt2)^2}`

`=|sqrt3+sqrt2|=sqrt3+sqrt2`

Answer 2

`7. sqrt(4+2sqrt3)`

`=sqrt{3+2sqrt3+1}`

`=sqrt{(sqrt3+1)^2}`

`=sqrt3+1`

`8. sqrt(4-2sqrt3)`

`=sqrt{3-2sqrt3+1}`

`=sqrt{(sqrt3-1)^2}`

`=sqrt3-1`

`9. sqrt(11-2sqrt(30))`

`=sqrt{6-2sqrt5sqrt6+5}`

`=sqrt{(sqrt6-sqrt5)^2}`

`=sqrt6-sqrt5`

`10. sqrt(21-4sqrt(17))`

`=sqrt{17-2.2.sqrt{17}+4}`

`=sqrt{(sqrt{17}-2)^2}`

`=sqrt{17}-2`