Racines

A = \(\sqrt{2}+3\sqrt{8}-6\sqrt{50}\)

B = \(\sqrt{2}+\sqrt{\dfrac{1}{2}}-\sqrt{\dfrac{1}{8}}\)

C = \(\dfrac{\sqrt{3}}{\sqrt{3}-2}\)

D = \(\dfrac{2\sqrt{21}\sqrt{75a^{2}}}{\sqrt{35}\sqrt{20}}\)

E = \(\left(\dfrac{\sqrt{10-2\sqrt{5}}}{4}\right)^{2}+\left(\dfrac{1+\sqrt{5}}{4}\right)^{2}\)

F = \((\sqrt{2}+\sqrt{7})^{3}\)

G = \((2a+\sqrt{b})^{2}+(1-2a\sqrt{b})^{2}-(2a\sqrt{b})^{2}\)

H = \(\dfrac{\sqrt{3}}{\sqrt{3}-\dfrac{2}{\sqrt{3}-\dfrac{2}{\sqrt{3}}}}\)

I = \(\dfrac{3\sqrt{5}+\sqrt{20}}{\sqrt{45}\left(2-\dfrac{5}{6}+\dfrac{4}{3}\right)(1-\sqrt{3})}\)

J = \((4+3\sqrt{2})^{2}-(2+\sqrt{2})(\sqrt{2}-1)\)

K = \(\sqrt{\dfrac{7+4\sqrt{3}}{7-4\sqrt{3}}}+\sqrt{\dfrac{7-4\sqrt{3}}{7+4\sqrt{3}}}\)

L = \(\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}\)

M = \(\dfrac{\sqrt{0,04}}{\sqrt{0,0016}}+\dfrac{\sqrt{0,01}}{\sqrt{0,04}}\)

N = \(\left(\sqrt{2-\sqrt{2}}+\sqrt{2+\sqrt{2}}\right)^{2}\)

O = \(\sqrt{\dfrac{a^{6}+a^{6}+a^{6}+a^{6}}{5^{2}+5^{2}+5^{2}+5^{2}}}\)

P = \(\sqrt{6-\sqrt{6-\sqrt{6-\sqrt{6-\sqrt{\dfrac{4\sqrt{27}}{3\sqrt{3}}}}}}}\)

Q = \(\sqrt{\dfrac{48a^{6}b^{12}}{243(ab)^{4}}}\)

R = \(\sqrt{\dfrac{4^{80}+5\times 8^{53}}{28\times 2^{155}}}\)

S = \(\left(\sqrt{1+\sqrt{1-a^{2}}}+\sqrt{1-\sqrt{1-a^{2}}}\right)^{2}\) \((a \in [0\,;\,1])\)