Question

calculati: a) √(1-√2)^2 + √(√2-√3)^2 + √(√3-√4)^2

Answer 1

..................................

Answer 2

$\sqrt{(1-\sqrt2)^2} + \sqrt{(\sqrt2-\sqrt3)^2} + \sqrt{(\sqrt3-\sqrt4)^2} = \\ \\ = |1-\sqrt2|+|\sqrt2-\sqrt3|+|\sqrt3-\sqrt4| = \\ \\ =(\sqrt2-1)+(\sqrt3-\sqrt2)+(\sqrt4-\sqrt3) = \\ \\ = \sqrt2-1+\sqrt3-\sqrt2+\sqrt4-\sqrt3 = \\ \\ = -1+\sqrt4 = \\ \\ =\sqrt4-1$