How do you simplify (sqrt11-3)(sqrt11+3)?

1 Answer
Apr 16, 2018

The result is $2$.

Explanation:

Use the FOIL method to expand the parentheses:

$\textcolor{w h i t e}{=} \left(\sqrt{11} - 3\right) \left(\sqrt{11} + 3\right)$

$= \sqrt{11} \cdot \sqrt{11} + 3 \sqrt{11} - 3 \sqrt{11} - 3 \cdot 3$

$= \sqrt{11} \cdot \sqrt{11} \textcolor{red}{\cancel{\textcolor{b l a c k}{\textcolor{b l a c k}{+} 3 \sqrt{11} - 3 \sqrt{11}}}} - 3 \cdot 3$

$= \sqrt{11} \cdot \sqrt{11} - 3 \cdot 3$

$= \sqrt{11} \cdot \sqrt{11} - 9$

$= {\left(\sqrt{11}\right)}^{2} - 9$

$= 11 - 9$

$= 2$

You can check this using a calculator:

Hope this helped!