Question

Câu 1. (2,0 điểm) Thực hiện phép tính:

a) $\sqrt{20}+2 \sqrt{45}-3 \sqrt{80}+\sqrt{125}$.

b) $\dfrac{2 \sqrt{3}+3 \sqrt{2}}{\sqrt{3}+\sqrt{2}}-4 \sqrt{\dfrac{3}{2}}-\dfrac{5}{1-\sqrt6}$.

c) $\dfrac{\sqrt{x}}{\sqrt{x}-2}-\dfrac{4(\sqrt{x}-1)}{x-2 \sqrt{x}}$ với $x \neq 4, x>0$.

Answer 1

a) \(\sqrt{ }\)20 + 2\(\sqrt{ }\)45 - 3\(\sqrt{ }\)80 + \(\sqrt{ }\)125

= \(\sqrt{ }\)4.5 +2\(\sqrt{ }\)9.5 - 3\(\sqrt{16.5}\)

= 2\(\sqrt{5}\) + 6\(\sqrt{5}\) - 12\(\sqrt{5}\)

= -4\(\sqrt{5}\)

b) \(\dfrac{2\sqrt{3}+3\sqrt{2}}{\sqrt{3}+\sqrt{2}}\) - \(4\sqrt{\dfrac{3}{2}}\)- \(\dfrac{5}{1-\sqrt{6}}\)

= \(\dfrac{2\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{3}+\sqrt{2}}\)- \(\sqrt{16.\dfrac{3}{2}}\) - \(\dfrac{5\left(1+\sqrt{6}\right)}{\left(1-\sqrt{6}\right)\left(1+\sqrt{6}\right)}\)

= 2 - \(\sqrt{24}\) - \(\dfrac{5\left(1+\sqrt{6}\right)}{1-6}\)

= 2 - \(\sqrt{4.6}\) + 1+\(\sqrt{ }\)6

= 2 - 2\(\sqrt{ }\)6 + 1+\(\sqrt{ }\)6

= 3 - \(\sqrt{ }\)6

c) (đề bài) với x khác 4...

= \(\dfrac{\sqrt{x}}{\sqrt{x}-2}\)- \(\dfrac{4\left(\sqrt{x}-1\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\)

= \(\dfrac{x}{\sqrt{x}\left(\sqrt{x}-2\right)}\)- ....

= \(x-4\sqrt{x}+4\)/ \(\sqrt{x}\left(\sqrt{x}-2\right)\)

= (căn -2)²/ căn x(căn x -2)

= căn x-2/căn x

Answer 2

a) căn 5

 

Answer 3

Bài 1:

a) \(\sqrt{20}+2\sqrt{45}-3\sqrt{80}+\sqrt{125}\)

  = \(2\sqrt{5}+6\sqrt{5}-12\sqrt{5}+5\sqrt{5}\)

  = \(\sqrt{5}\)

b) \(\dfrac{2\sqrt{3}+3\sqrt{2}}{\sqrt{3}+\sqrt{2}}-4\sqrt{\dfrac{3}{2}}-\dfrac{5}{1-\sqrt{6}}\)

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

  = \(\sqrt{6}-\sqrt{6}+1=1\)

c) \(\dfrac{\sqrt{x}}{\sqrt{x}-2}-\dfrac{4\left(\sqrt{x}-1\right)}{x-2\sqrt{x}}\) (ĐKXĐ: x > 0; x ≠ 4)

  = \(\dfrac{x-4\sqrt{x}+4}{x-2\sqrt{x}}\)

  = \(\dfrac{\left(\sqrt{x}-2\right)^2}{\sqrt{x}\left(\sqrt{x}-2\right)}\)

  = \(\dfrac{\sqrt{x}-2}{\sqrt{x}}\)

Answer 4

2