Question

[Trịnh Trọng Khánh]

Bài 1 Rút gọn các biểu thức

a, \(-\sqrt{36b}-\frac{1}{3}\sqrt{54b}+\frac{1}{5}\sqrt{150b}\)     với b>0

b,\(\frac{3+\sqrt{4}}{\sqrt{6}+\sqrt{2}-\sqrt{5}}\)

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

d,   A=\(\sqrt{\sqrt{5}-\sqrt{\sqrt{3}-\sqrt{29-6\sqrt{20}}}}\)

e,   B=\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(=-6\sqrt{b}-\dfrac{1}{3}\cdot3\sqrt{3b}+\dfrac{1}{5}\cdot5\sqrt{6b}\)

\(=-6\sqrt{b}-\sqrt{3}\cdot\sqrt{b}+\sqrt{6}\cdot\sqrt{b}\)

\(=\sqrt{b}\left(-6-\sqrt{3}+\sqrt{6}\right)\)

c: \(=\sqrt{\left(5+2\sqrt{6}\right)^2}+\sqrt{\left(5-2\sqrt{6}\right)^2}\)

\(=5+2\sqrt{6}+5-2\sqrt{6}=10\)

d: \(A=\sqrt{\sqrt{5}-\sqrt{3-2\sqrt{5}+3}}\)

\(=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)

\(=\sqrt{\sqrt{5}-\sqrt{5}+1}=1\)

e: \(B=\sqrt{6+2\sqrt{5-2\sqrt{3}-1}}\)

\(=\sqrt{6+2\cdot\left(\sqrt{3}-1\right)}=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)