Question

Rút gọn:

a)\(2\sqrt{3x}-4\sqrt{3x}\)+\(27-2\sqrt{3x}\)(\(x\ge0\))

b)\(3\sqrt{2x}-5\sqrt{8x}\)+\(7\sqrt{8x}+28\)\(\left(x\ge0\right)\)

c)\(\frac{2}{x^2-y^2}\sqrt{\frac{3\left(x+y\right)^2}{2}}\)\(\left(x\ge0,y\ge0,x\ne y\right)\)

d)\(\frac{2}{2a-1}\sqrt{5a^2\left(1-4a+4a^2\right)}\)

Answer 1

a) \(2\sqrt{3x}-4\sqrt{3x}+27-2\sqrt{3x}=27-4\sqrt{3x}\)

b) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{8x}+28=3\sqrt{2x}+2\sqrt{8x}+28=3\sqrt{2x}+4\sqrt{2x}+28=7\sqrt{2x}+28\)

c) \(\frac{2}{x^2-y^2}\sqrt{\frac{3\left(x+y\right)^2}{2}}=\frac{2}{\left(x-y\right)\left(x+y\right)}.\frac{\sqrt{3}\left|x+y\right|}{\sqrt{2}}=\frac{\sqrt{6}}{x-y}\)

d) \(\frac{2}{2a-1}\sqrt{5a^2\left(1-4x+4a^2\right)}=\frac{2}{2a-1}\sqrt{5a^2\left(2a-1\right)^2}=\frac{2}{2a-1}.\sqrt{5}\left|a\left(2a-1\right)\right|=2a\sqrt{5}\)

Thiếu ĐKXĐ : ..............

Answer 2

a) Ta có: \(2\sqrt{3x}-4\sqrt{3x}+27-2\sqrt{3x}\)

        \(=27-4\sqrt{3x}\)

b) Ta có: \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{8x}+28\)

        \(=3\sqrt{2x}-5.2\sqrt{2x}+7.2\sqrt{2x}+28\)

        \(=3\sqrt{2x}-10\sqrt{2x}+14\sqrt{2x}+28\)

        \(=7\sqrt{2x}+28\)

c) Ta có: \(\frac{2}{x^2-y^2}.\sqrt{\frac{3\left(x+y\right)^2}{2}}\)

        \(=\sqrt{\frac{4}{\left(x-y\right)^2.\left(x+y\right)^2}.\frac{3\left(x+y\right)^2}{2}}\)

        \(=\sqrt{\frac{2.3}{\left(x-y\right)^2}}\)

        \(=\frac{1}{x-y}.\sqrt{6}\)

d) Ta có: \(\frac{2}{2a-1}.\sqrt{5a^2.\left(1-4a+4a^2\right)}\)

        \(=\sqrt{\frac{4}{\left(2a-1\right)^2}.5a^2.\left(2a-1\right)^2}\)

        \(=2a.\sqrt{5}\)