\(6\pm2\sqrt{5}=5\pm2.\sqrt{5}.1+1=\left(\sqrt{5}\pm1\right)^2\)
\(\Rightarrow M=\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}=\sqrt{\left(\sqrt{5}+1\right)^2}-\sqrt{\left(\sqrt{5-1}\right)^2}=\sqrt{5}+1-\sqrt{5}+1=2\)
Rút gọn rồi tính:
a) \(5\sqrt{\left(-2\right)^4}\) c)\(\sqrt{\sqrt{\left(-5\right)^8}}\)
b)\(-4\sqrt{\left(-3\right)^6}\)
Bài 1 :Chứng minh các đẳng thức :
a ) \(2\sqrt{2}\left(\sqrt{3}-2\right)\) + \(\left(1+2\sqrt{2}\right)^2-2\sqrt{6}=9\)
b ) \(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}=\sqrt{6}\)
c ) \(\sqrt{11-6\sqrt{2}}+\sqrt{11+6\sqrt{2}}=6\)
Bài 2 : Rút gọn các biểu thức sau :
a ) \(\frac{1}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{5}-\sqrt{3}}\)
b ) \(\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{6}-\sqrt{2}}\)
c ) \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)
Bài 3 : Rút gọn các biểu thức sau :
a ) \(\sqrt{20}-\sqrt{45}+3\sqrt{18}+\sqrt{72}\)
b ) \(\left(\sqrt{28}-2\sqrt{3}+\sqrt{7}\right)\sqrt{7}+\sqrt{84}\)
c ) \(\left(\sqrt{6}+\sqrt{5}\right)^2-\sqrt{120}\)
d ) \(\left(\frac{1}{2}\sqrt{\frac{1}{2}}-\frac{3}{2}\sqrt{2}+\frac{4}{5}\sqrt{200}\right):\frac{1}{8}\)
Bài 2 : Rút gọn biểu thức sau A = sqrt(5 - 2sqrt(6)) - sqrt((sqrt(2) - sqrt(3)) ^ 2)
2.4 Rút gọn biểu thức
\(a,\dfrac{3-\sqrt{x}}{x-9}\) ( vs x ≥ 0, x≠ 9)
b, \(\dfrac{x-5\sqrt{x}+6}{\sqrt{x}-3}\)( vs x ≥ 0 ; x ≠ 9)
c, \(6-2x-\sqrt{9-6x+x^2}\left(x< 3\right)\)
Rút gọn biểu thức
a)\(\sqrt{26+15\sqrt{3}}\).
b)\(\sqrt{2-\sqrt{3}}\)
c)\(\left(\sqrt{10}-\sqrt{2}\right)\left(\sqrt{3+5}\right)\)
d)\(\left(\sqrt{6}-2\right)\left(5+\sqrt{24}\right)\sqrt{5-\sqrt{24}}\)
Rút gọn rồi tính :
a) \(5\sqrt{\left(-2\right)^4}\)
b) \(-4\sqrt{\left(-3\right)^6}\)
c) \(\sqrt{\sqrt{\left(-5\right)^8}}\)
d) \(2\sqrt{\left(-5\right)^6}+3\sqrt{\left(-2\right)^8}\)
Tìm x để căn thức sau có nghĩa:
\(\sqrt{\dfrac{-5}{x^2+6}}\)
2. Rút gọn rồi tính:
a) \(5\sqrt{\left(-2\right)^4}\)
b)\(-4\sqrt{\left(-3\right)}^6\)
c) \(\sqrt{\sqrt{\left(-5\right)}}^8\)
d) \(2\sqrt{\left(-5\right)}^6+3\sqrt{\left(-2\right)}^8\)
Rút gọn
a.\(\dfrac{\sqrt{7}-5}{2}-\dfrac{6}{\sqrt{7}-2}+\dfrac{1}{3+\sqrt{7}}+\dfrac{3}{5+2\sqrt{7}}\)
b.\(\left(\sqrt{10}+\sqrt{2}\right).\left(6-2\sqrt{5}\right).\sqrt{3+\sqrt{5}}\)
Rút gọn :
a) \(\left(\sqrt{6}+\sqrt{2}\right).\left(\sqrt{3}-2\right)\left(\sqrt{2+\sqrt{3}}\right)\)
b) \(\sqrt{2}.\left(\sqrt{2-\sqrt{3}}\right).\left(\sqrt{3}+1\right)\)
c) \(\left(\sqrt{10}-\sqrt{6}\right).\left(\sqrt{4-\sqrt{15}}\right)\)
d)\(\left(\sqrt{3}-\sqrt{12}\right).\left(\sqrt{5+2\sqrt{6}}\right)\)
e) \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}-\sqrt{2}\right).\left(2+\sqrt{3}\right)\)
f) \(\sqrt{4+\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}\)
