Question

Rút gọn:

\(\)\(a,\sqrt{40}-2\sqrt{250}+3\sqrt{90}\)

\(b,\frac{-1}{4+3\sqrt{2}}+\frac{1}{4-3\sqrt{2}}\)

\(c,\left(3\sqrt{2}+\sqrt{10}\right).\sqrt{7-\sqrt{45}}\)

\(d,\sqrt{18}-\sqrt{32}+\sqrt{50}\)

e,\(\sqrt{19+8\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)

Answer 1

a/ \(2\sqrt{10}-10\sqrt{10}+9\sqrt{10}=\sqrt{10}\)

b/ \(\frac{-1\left(4-3\sqrt{2}\right)+1\left(4+3\sqrt{2}\right)}{\left(4-3\sqrt{2}\right)\left(4+3\sqrt{2}\right)}=\frac{-4+3\sqrt{2}+4+3\sqrt{2}}{16-18}=\frac{6\sqrt{2}}{-2}=-3\sqrt{2}\)

c/ \(\left(3+\sqrt{5}\right).\sqrt{2}.\sqrt{7-3\sqrt{5}}=\left(3+\sqrt{5}\right)\sqrt{14-6\sqrt{5}}\)

\(=\left(3+\sqrt{5}\right)\sqrt{\left(3-\sqrt{5}\right)^2}=\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)=9-5=4\)

d/ \(3\sqrt{2}-4\sqrt{2}+5\sqrt{2}=4\sqrt{2}\)

e/ \(\sqrt{19+8\sqrt{3}}+\sqrt{7-4\sqrt{3}}=\sqrt{\left(4+\sqrt{3}\right)^2}+\sqrt{\left(2-\sqrt{3}\right)^2}\)

\(=4+\sqrt{3}+2-\sqrt{3}=6\)

Answer 2