Question

Thực hiện phép tính:

a) \(\left(\frac{1}{7-4\sqrt{3}}+\frac{3}{7+4\sqrt{3}}\right)\left(7+2\sqrt{3}\right)\)

b)\(\left(\frac{3\sqrt{5}-\sqrt{15}}{\sqrt{27}-3}+\frac{2\sqrt{5}}{\sqrt{3}}\right).4\sqrt{15}\)

c)\(\sqrt{5-2\sqrt{6-25-\sqrt{96}}}\)

d)\(\sqrt{23-2\sqrt{112}}+\sqrt{23+2\sqrt{112}}\)

Answer 1

a/ \(=\left(7+4\sqrt{3}+3\left(7-4\sqrt{3}\right)\right)\left(7+2\sqrt{3}\right)\)

\(=\left(28-8\sqrt{3}\right)\left(7+2\sqrt{3}\right)\)

\(=4\left(7-2\sqrt{3}\right)\left(7+2\sqrt{3}\right)\)

\(=4\left(49-12\right)=...\)

b/ \(=\left(\frac{\sqrt{15}\left(\sqrt{3}-1\right)}{3\left(\sqrt{3}-1\right)}+\frac{2\sqrt{15}}{3}\right).4\sqrt{15}\)

\(=\left(\frac{\sqrt{15}}{3}+\frac{2\sqrt{15}}{3}\right).4\sqrt{15}\)

\(=\sqrt{15}.4\sqrt{15}=4.15=...\)

c/ Bạn coi lại đề

d/ \(\sqrt{23-2\sqrt{112}}+\sqrt{23+2\sqrt{112}}\)

\(=\sqrt{\left(4-\sqrt{7}\right)^2}+\sqrt{\left(4+\sqrt{7}\right)^2}\)

\(=4-\sqrt{7}+4+\sqrt{7}=8\)