Question

How do you simplify `(sqrt3 - sqrt5)(sqrt3-sqrt5)`?

Answer 1

`8 - 2sqrt15`

Explanation:

Use FOIL (First, Outside, Inside, Last) to multiply the binomials.

(`sqrt3 - sqrt5`)(`sqrt3-sqrt5`)

Remember that the negative sign is part of the `sqrt5` term.

First:
(`color(red)sqrt3 - sqrt5`)(`color(red)sqrt3 - sqrt5`)
`sqrt3 * sqrt3 = 3`

Outside:
(`color(red)sqrt3 - sqrt5`)(`sqrt3 color(red) (-sqrt5`)
`sqrt3 * sqrt5 = sqrt(3*5) = -sqrt 15`

Inside:
(`sqrt3 color(red)(-sqrt5`)(`color(red)sqrt3 - sqrt5`)
`sqrt5 * sqrt3 = sqrt(5*3) = -sqrt15`

Last:
(`sqrt3 color(red)(-sqrt5`)(`sqrt3 color(red)(-sqrt5`)
`sqrt5 * sqrt5 = 5`

Add all the terms together and simplify.
`3 - sqrt15 - sqrt15 + 5`
`3 - 2sqrt15 + 5`
`8 - 2sqrt15`

Answer 2

8- 2`sqrt15`

Explanation:

FOIL (First, Inner, Outer, Last)

1. Multiply √3 by √3 to get √9.
2. Multiply √3 by −√5 to get −√15
3. Multiply √3 by −√5 to get −√15
   4.Multiply −√5 by −√5 to get √25
4. Simplify √9 and √25
5. Add 3 and 5 (=8)
6. Add like terms (−√15−√15= −2√15)

      (√3−√5)(√3−√5)
   

   1-4) √9−√15−√15+√25
   5) 3−√15−√15+5
   6) 8−√15−√15
   7) 8−2√15