Question

Escreva $\sqrt{17+12 \sqrt{2} }$ na forma √A + B 


Alguém poderia me ajudar? ; )

Answer 1

$(3 +2\sqrt{2})^2 = 3^2 + 2\cdot 3\cdot2\sqrt{2}+(2\sqrt{2})^2\\ (3 +2\sqrt{2})^2 = 9 + 12\sqrt{2}+8\\(3 +2\sqrt{2})^2 = 17 + 12\sqrt{2}\\ (3 +2\sqrt{2})^2 = 9 + 12\sqrt{2}+\\ (3 +\sqrt{2\cdot2^2})^2 = 17 + 12\sqrt{2}\\ (3 +\sqrt{8})^2 = 17 + 12\sqrt{2}\\ \\ \\ \sqrt{17+12\sqrt{2}}=\sqrt{(3 +\sqrt{8})^2}=3 +\sqrt{8}=\sqrt{8}+2$