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

Apr 16, 2017

$8 - 2 \sqrt{15}$

#### Explanation:

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

($\sqrt{3} - \sqrt{5}$)($\sqrt{3} - \sqrt{5}$)

Remember that the negative sign is part of the $\sqrt{5}$ term.

First:
($\textcolor{red}{\sqrt{3}} - \sqrt{5}$)($\textcolor{red}{\sqrt{3}} - \sqrt{5}$)
$\sqrt{3} \cdot \sqrt{3} = 3$

Outside:
($\textcolor{red}{\sqrt{3}} - \sqrt{5}$)(sqrt3 color(red) (-sqrt5)
$\sqrt{3} \cdot \sqrt{5} = \sqrt{3 \cdot 5} = - \sqrt{15}$

Inside:
(sqrt3 color(red)(-sqrt5)($\textcolor{red}{\sqrt{3}} - \sqrt{5}$)
$\sqrt{5} \cdot \sqrt{3} = \sqrt{5 \cdot 3} = - \sqrt{15}$

Last:
(sqrt3 color(red)(-sqrt5)(sqrt3 color(red)(-sqrt5)
$\sqrt{5} \cdot \sqrt{5} = 5$

Add all the terms together and simplify.
$3 - \sqrt{15} - \sqrt{15} + 5$
$3 - 2 \sqrt{15} + 5$
$8 - 2 \sqrt{15}$

Apr 16, 2017

8- 2$\sqrt{15}$

#### 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