BÀi 1:

\(\sqrt{\frac43}+\sqrt{12}-\frac43\cdot\sqrt{\frac34}\)

\(=\sqrt{\frac{12}{9}}+\sqrt{12}-\frac43\cdot\frac{\sqrt{12}}{4}\)

\(=\frac{2\sqrt3}{3}+2\sqrt3-\frac{2\sqrt3}{3}=2\sqrt3\)

Bài 2:

a: \(\left(2-a\right)\cdot\sqrt{\frac{2a}{a-2}}\)

\(=-\left(a-2\right)\cdot\sqrt{\frac{2a}{a-2}}\)

\(=-\sqrt{\frac{2a\left(a-2\right)^2}{a-2}}=-\sqrt{2a\left(a-2\right)}\)

b: \(\left(x-5\right)\cdot\sqrt{\frac{x}{25-x^2}}=-\left(5-x\right)\cdot\sqrt{\frac{x}{25-x^2}}=-\sqrt{\frac{x}{\left(5-x\right)\left(5+x\right)}\cdot\left(5-x\right)^2}\)

\(=-\sqrt{\frac{x\left(5-x\right)}{5+x}}\)

c: \(\left(a-b\right)\cdot\sqrt{\frac{3a}{b^2-a^2}}=-\left(b-a\right)\cdot\sqrt{\frac{3a}{\left(b-a\right)\left(b+a\right)}}\)

\(=-\sqrt{\frac{3a\left(b-a\right)^2}{\left(b-a\right)\left(b+a\right)}}=-\sqrt{\frac{3a\left(b-a\right)}{b+a}}\)

a, Để A nhận giá trị dương thì \(A>0\)hay \(x-1>0\Leftrightarrow x>1\)

b, \(B=2\sqrt{2^2.5}-3\sqrt{3^2.5}+4\sqrt{4^2.5}\)

\(=4\sqrt{5}-9\sqrt{5}+16\sqrt{5}=\left(4-9+16\right)\sqrt{5}=11\sqrt{5}\)

( theo công thức \(A\sqrt{B}=\sqrt{A^2B}\))

c, Với \(a\ge0;a\ne1\)

\(C=\left(\frac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1-\sqrt{a}}{1-a}\right)^2\)

\(=\left(\frac{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)}{1-\sqrt{a}}+\sqrt{a}\right)\left(\frac{1-\sqrt{a}}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}\right)^2\)

\(=\left(\sqrt{a}+1\right)^2.\frac{1}{\left(\sqrt{a}+1\right)^2}=1\)

\(\sqrt{48\cdot45}=12\sqrt{15}\\ \sqrt{225\cdot17}=15\sqrt{17}\\ \sqrt{a^3b^7}=\left|ab^3\right|\sqrt{ab}=ab^3\sqrt{ab}\\ \sqrt{x^5\left(x-3\right)^2}=\left|x^2\left(x-3\right)\right|\sqrt{x}=x^2\left(x-3\right)\sqrt{x}\)

\(\sqrt{48\cdot45}=4\sqrt{3}\cdot3\sqrt{5}=12\sqrt{15}\)

\(\sqrt{225\cdot17}=15\sqrt{17}\)

đưa thừa số vào trong dấu căn*

mình nhầm

a: \(a^2\cdot\sqrt{\dfrac{2}{3a}}=a^2\cdot\dfrac{\sqrt{2}}{\sqrt{3}\cdot\sqrt{a}}=\dfrac{a\sqrt{2}}{\sqrt{3}}=\dfrac{a\sqrt{6}}{3}\)

b: \(\dfrac{x-3}{x}\cdot\sqrt{\dfrac{x^3}{9-x^2}}\)

\(=\dfrac{x-3}{x}\cdot\dfrac{x\sqrt{x}}{\sqrt{x-3}\cdot\sqrt{x+3}}\)

\(=\dfrac{\sqrt{x}\cdot\sqrt{x-3}}{\sqrt{x+3}}\)

\(\frac{1}{x-y}.\sqrt{x^4\left(x^2+y^2-2xy\right)}\)

\(=\frac{1}{x-y}.\sqrt{\left(x^2\right)^2.\left(x-y\right)^2}\)

\(=\frac{1}{x-y}\left(x-y\right)x^2\)

\(=x^2\)

a,\(-\sqrt{10x^2\cdot y\left(3-\sqrt{2}\right)^2}=-\left|x\right|\) \(\cdot\left(3-\sqrt{2}\right)\cdot\sqrt{10y}\)

xet th \(x\ge0\) ta co \(-x\cdot\left(3-\sqrt{2}\right)\sqrt{10y}\)

xet th \(x< 0\) ta có \(x\left(3-\sqrt{2}\right)\sqrt{10y}\)

b,\(\sqrt{3\left(x^2-2xy+y^2\right)}=\) \(\sqrt{3\cdot\left(x-y\right)^2}=\left|x-y\right|\sqrt{3}\)

a) \(\sqrt{27\left(9-4\sqrt{5}\right)}=3\sqrt{3\left(\sqrt{5}-2\right)^2}=3\sqrt{3}\left(\sqrt{5}-2\right)=3\sqrt{15}-6\sqrt{3}\)

b) \(\sqrt{a^4b^5}=a^2b^2\sqrt{b}\)

c) \(\sqrt{a^3\left(1-a\right)^4}=a\left(1-a\right)^2\sqrt{a}\)

d) không biết

\(x\sqrt{\dfrac{2}{x}}=\sqrt{x^2\cdot\dfrac{2}{x}}=\sqrt{2x}\)

\(x\sqrt{\dfrac{2}{5}}=\sqrt{\dfrac{2}{5}\cdot x^2}=\sqrt{\dfrac{2x^2}{5}}\)

\(\left(x-5\right)\cdot\sqrt{\dfrac{x}{25-x^2}}=\sqrt{\left(x-5\right)^2\cdot\dfrac{x}{-\left(x-5\right)\left(x+5\right)}}=\sqrt{-\dfrac{x\left(x-5\right)}{x+5}}\)

\(x\sqrt{\dfrac{7}{x^2}}=\sqrt{x^2\cdot\dfrac{7}{x^2}}=\sqrt{7}\)