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

2 Answers
Apr 16, 2017

Answer:

#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#

Apr 16, 2017

Answer:

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