Expand the Roots

Algebra Level 1

Evaluate

( 2 + 2 ) ( 2 − 1 ) ( 2 + \sqrt{2} ) ( \sqrt{2} - 1 )

2 − 1 \sqrt{2} - 1 2 − 2 2 - \sqrt{2} 2 + 1 \sqrt{2} + 1 2 \sqrt{2}

Chung Kevin by Chung Kevin , 46, Australia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Sharky Kesa
Nov 9, 2016

( 2 + 2 ) ( 2 − 1 ) = ( 2 × ( 2 + 1 ) ) ( 2 − 1 ) = 2 × ( 2 + 1 ) ( 2 − 1 ) = 2 × ( 2 2 − 1 2 ) = 2 × ( 2 − 1 ) = 2 \begin{aligned} (2+\sqrt{2})(\sqrt{2}-1) &= (\sqrt{2} \times (\sqrt{2} + 1))(\sqrt{2} - 1)\\ & = \sqrt{2} \times (\sqrt{2}+1)(\sqrt{2}-1)\\ &= \sqrt{2} \times (\sqrt{2}^2 - 1^2)\\ &= \sqrt{2} \times (2-1)\\ &= \sqrt{2} \end{aligned}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...