Question

√(19-6√2)+√(43-30√2)

Answer 1

$\sqrt{19 - 6\sqrt2} + \sqrt{43 - 30\sqrt2}=$

$\sqrt{18 - 2\cdot3\sqrt2\cdot1+1} + \sqrt{25-2\cdot5\cdot3\sqrt2+18}=$

$\sqrt{(\sqrt{18})^2 - 2\cdot3\sqrt2\cdot1+1^2} + \sqrt{5^2-2\cdot5\cdot3\sqrt2+(\sqrt{18})^2}=$

$\sqrt{(3\sqrt{2})^2 - 2\cdot3\sqrt2\cdot1+1^2} + \sqrt{5^2-2\cdot5\cdot3\sqrt2+(3\sqrt{2})^2}=$

$\sqrt{(3\sqrt{2}-1)^2} + \sqrt{(5-3\sqrt{2})^2}=$

$|3\sqrt{2}-1| + |5-3\sqrt{2}|=$

$3\sqrt{2}-1 + 5-3\sqrt{2}=4$