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

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Answer 1 · 2017-04-16T22:00:12

$8 - 2sqrt15$

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 · 2017-04-16T22:12:44

8- 2 $sqrt15$

FOIL (First, Inner, Outer, Last)

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