Root plus root

Algebra Level 3

2 + 2 + 2 3 \large \sqrt[3]{2 + \sqrt{2 + \sqrt2} }

What is the approximate value of the expression above?

1.962 1.414 1.567 1.852 4 2

Αλέξανδρος Μυλωνάς by Αλέξανδρος Μυλωνάς , 20, Greece

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

Kay Xspre
Mar 24, 2016

I will use a rough estinates. As 1.4 < 2 < 1.5 1.4 < \sqrt{2} < 1.5 We get 3.4 < 2 + 2 < 3.5 3.4 < 2+\sqrt{2} < 3.5 Or simply (roughly) 1.8 < 2 + 2 < 1.9 1.8 < \sqrt{2+\sqrt{2}} < 1.9 3.8 < 2 + 2 + 2 < 3.9 3.8 < 2+\sqrt{2+\sqrt{2}} < 3.9 1.5 < 2 + 2 + 2 3 < 1.6 1.5 < \sqrt[3]{2+\sqrt{2+\sqrt{2}}} < 1.6

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Excellent solution!

Αλέξανδρος Μυλωνάς - 5 years, 2 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...