Question

√(19-6√2)+√(43-30√2)

Answer 1

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

$sqrt{18 - 2cdot3sqrt2cdot1+1} + sqrt{25-2cdot5cdot3sqrt2+18}=$

$sqrt{(sqrt{18})^2 - 2cdot3sqrt2cdot1+1^2} + sqrt{5^2-2cdot5cdot3sqrt2+(sqrt{18})^2}=$

$sqrt{(3sqrt{2})^2 - 2cdot3sqrt2cdot1+1^2} + sqrt{5^2-2cdot5cdot3sqrt2+(3sqrt{2})^2}=$

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

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

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