A = \(\sqrt{48}-2\sqrt{75}+\sqrt{108}-\dfrac{1}{7}\sqrt{147}\)
= \(\sqrt{16.3}-2\sqrt{25.3}+\sqrt{36.3}-\dfrac{1}{7}\sqrt{49.3}\)
= \(4\sqrt{3}-10\sqrt{3}+6\sqrt{3}-\sqrt{3}\)
= \(-\sqrt{3}\)
Rút gọn: \(\dfrac{5\sqrt{a}-3}{\sqrt{a}-2}+\dfrac{3\sqrt{a}+1}{\sqrt{a}+2}+\dfrac{a^2+2\sqrt{a}+8}{4-a}\)
Rút gọn:
\(A=1-\left[\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}+\dfrac{2x-1+\sqrt{x}}{1-x}\right]\cdot\left[\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\right]\)
\(B=\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}}\right):\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}-1}\right)\)
a) Rút gọn B
b) x bằng mấy để \(\left|B\right|=B\)
Rút gọn:
\(B=2\sqrt{18}-4\sqrt{32}+\sqrt{72}+3\sqrt{8}\)
\(C=\dfrac{\sqrt{8-2\sqrt{15}}-\sqrt{5}}{\dfrac{1}{\sqrt{3}-2}-\dfrac{1}{\sqrt{3}+2}}\)
Rút gọn rồi tìm a để \(\sqrt{a}>A\)
\(A=\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\cdot\left(\sqrt{a}-\dfrac{1}{\sqrt{a}}\right)\)
Tìm điều kiện xác định và rút gọn các biểu thức sau :
a/ \(A=\left(\dfrac{\sqrt{3}}{x^2+x\sqrt{3}+3}+\dfrac{3}{x^3-\sqrt{27}}\right).\left(\dfrac{x}{\sqrt{3}}+\dfrac{\sqrt{3}}{x}+1\right)\)
b/ \(B=\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{x^2+\sqrt{x}}{x-\sqrt{x}+1}+x+1\)
c/ \(C=\left(\dfrac{2+\sqrt{x}}{x+2\sqrt{x}+1}-\dfrac{\sqrt{x}-2}{x-1}\right).\dfrac{x\sqrt{x}+x-\sqrt{x}-1}{\sqrt{x}}\)
d/ \(\left[\dfrac{1}{x-1}+\dfrac{x^2+1-2x}{\left(x-1\right)^2+3x}-\dfrac{1+4x-2x^2}{x^3-1}\right]:\dfrac{2}{x^2+1}\)
Thu gọn:
a) \(\sqrt{7-4\sqrt{3}}-\sqrt{7+4\sqrt{3}}\)
b) \(\left(\frac{\sqrt{x}+1}{x-4}-\frac{\sqrt{x}-1}{x+4\sqrt{x}+4}\right)\cdot\frac{x\sqrt{x}+2x-4\sqrt{x}-8}{\sqrt{x}}\)
a,\(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1-1}}\)-\(\dfrac{\sqrt{3}}{\sqrt{\sqrt{3}+1+1}}\)
b,\(\dfrac{1}{\sqrt{7-\sqrt{24}+1}}\)-\(\dfrac{1}{\sqrt{7+\sqrt{24}+1}}\)
a,\(\dfrac{1}{\sqrt{7-\sqrt{24}+1}}\)-\(\dfrac{1}{\sqrt{7+\sqrt{24}-1}}\)
b,\(\dfrac{1}{3-\sqrt{7}}\)-\(\dfrac{1}{3+\sqrt{7}}\)
c,\(\sqrt{21+6\sqrt{6}}\)+\(\sqrt{21-6\sqrt{6}}\)