Question

How to simplify 2/√(2+√2)

Answer 1

`(2)/(√(2+\sqrt2))=(2)/(√(2+\sqrt2))\cdot(√(2-\sqrt2))/(√(2-\sqrt2))`

use √(ab) = √a · √b

`=(2√(2-\sqrt2))/(√((2+\sqrt2)(2-\sqrt2)))`

use (a + b)(a - b) = a² - b²

`=(2√(2-\sqrt2))/(√(2^2-(\sqrt2)^2))=(2√(2-\sqrt2))/(√(4-2))=(2√(2-\sqrt2))/(\sqrt2)\cdot(\sqrt2)/(\sqrt2)`

use √a · √a = a and √(ab) = √a · √b

`=(2√(2\cdot2-\sqrt2\cdot2))/(2)=√(4-2\sqrt2)\\\\Answer:\ \boxed{(2)/(√(2+\sqrt2))=√(4-2\sqrt2)}`