Question

How do you simplify `(3+ sqrt 5) times (5- sqrt5)`?

Answer 1

`10+2sqrt5`

Explanation:

By expanding the brackets using FOIL or similar method.

`rArr(3+sqrt5)(5-sqrt5)=15-3sqrt5+5sqrt5-(sqrt5)^2`
`"---------------------------------------------------------------"`

now in general `sqrtaxxsqrta=a`

`rArr(sqrt5)^2=sqrt5xxsqrt5=5`

radicals may be collected together in a similar manner to 'collecting like terms' algebraically.

That is `4sqrt3+5sqrt3=(4+5)sqrt3=9sqrt3`

`rArr-3sqrt5+5sqrt5=(-3+5)sqrt5=2sqrt5`
`"---------------------------------------------------------------"`

`rArr(3+sqrt5)(5-sqrt5)=15-3sqrt5+5sqrt5-(sqrt5)^2`

`=15+2sqrt5-5=10+2sqrt5`