How to compare numbers $\sqrt{5}-\sqrt{3}$ and $\sqrt{8-2\sqrt{15}}$

Question

How to compare the following numbers without using the calculator? $\sqrt{5}-\sqrt{3}$ and $\sqrt{8-2\sqrt{15}}$

See also: Denesting radicals at Wikipedia, Strategies to denest nested radicals (and the posts linked there). — Martin Sleziak, Oct 23 '16 at 23:05

score 3 · Answer 1 · answered Nov 20 '13 at 05:27

3

As $(\sqrt 5-\sqrt 3)^2=5+3-2\sqrt {15}$ they are equal

answered Nov 20 '13 at 05:27

Ross Millikan

score 0 · Answer 2 · answered Nov 20 '13 at 05:25

0

Hint:

$$\sqrt5-\sqrt3\ge\sqrt{8-2\sqrt{15}}\iff8-2\sqrt{15}\ge8-2\sqrt{15}\ldots$$

answered Nov 20 '13 at 05:25

DonAntonio

2 Answers2