Question

se considera nummarul a=$\sqrt{7+4\sqrt{3}}$+$\sqrt{(\sqrt{3}-2)^{2}}$. sa se arate ca a apartine lui N

Answer 1

$\it 7+4\sqrt3= 4+3=4\sqrt3=2^2+4\sqrt3+(\sqrt3)^2 = (2+\sqrt3)^2\\ \\ \\ (\sqrt3-2)^2=(2-\sqrt3)^2\\ \\ \\ a= \sqrt{(2+\sqrt3)^2} +\sqrt{(2-\sqrt3)^2} = |2+\sqrt3|+|2-\sqrt3| = 2+\sqrt3+2-\sqrt3=4$