Question

[nguyen thi khanh nguyen]

Thực hiện các phép tính sau:

a,\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)

b,\(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)

c,\(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)

d,\(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)

e,\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)

f,\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)

Giải giúp mình với m.n mình đang cần gấp lắm!!!!!

Answer 1

[Mysterious Person]

a) \(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}=\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}\)

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

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

b) \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}=\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\)

\(=\left|\sqrt{5}-\sqrt{2}\right|-\left|\sqrt{5}+\sqrt{2}\right|=\left(\sqrt{5}-\sqrt{2}\right)-\left(\sqrt{5}+\sqrt{2}\right)\)

\(=\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}=-2\sqrt{2}\)

c) \(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}=\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(=\left|\sqrt{3}-1\right|+\left|\sqrt{3}+1\right|=\left(\sqrt{3}-1\right)+\left(\sqrt{3}+1\right)\)

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

Answer 2

[Mysterious Person]

d) \(\sqrt{24+8\sqrt{5}}+\sqrt{9-4\sqrt{5}}=2\sqrt{6+2\sqrt{5}}+\sqrt{\left(\sqrt{5}-2\right)^2}\)

\(=2\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{5}-2=2\sqrt{5}+2+\sqrt{5}-2=3\sqrt{5}\)