Question

√(45+29√2)-√(45-29√2)

Answer 1

Формула: $sqrt{a+ sqrt{b} } pm sqrt{a- sqrt{b} } = sqrt{2apm2 sqrt{a^2-b} }$
$sqrt{45+29 sqrt{2}- sqrt{45-29 sqrt{2} } } = sqrt{2} cdot sqrt{45- sqrt{45^2-29^2cdot2} } = \ = sqrt{2(45- 7sqrt{7}) } = sqrt{90-14 sqrt{7} }$

Ответ: $sqrt{90-14 sqrt{7} }$