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

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

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

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

D, b nhân căn bậc 5 phần ab với a<0, b<0

a: \(13\sqrt{11}=\sqrt{13^2\cdot11}=\sqrt{1859}\)

b: \(-8\sqrt{2}=-\sqrt{64\cdot2}=-\sqrt{128}\)

c: \(a\sqrt{5a}=\sqrt{a^2\cdot5a}=\sqrt{5a^3}\)

d: \(b\sqrt{\dfrac{5}{ab}}=-\sqrt{b^2\cdot\dfrac{5}{ab}}=-\sqrt{\dfrac{5b}{a}}\)

a: \(xy^2\sqrt{x}=\sqrt{x^2y^4\cdot x}=\sqrt{x^3y^4}\)

b: \(\dfrac{2}{x}\sqrt{\dfrac{15xy}{4}}=-\sqrt{\dfrac{4}{x^2}\cdot\dfrac{15xy}{4}}=-\sqrt{\dfrac{15y}{x}}\)

1: \(3\sqrt8-5\sqrt{18}\)

\(=3\cdot2\sqrt2-5\cdot3\sqrt2\)

\(=6\sqrt2-15\sqrt2=-9\sqrt2\)

2:

\(7\sqrt3=\sqrt{7^2\cdot3}=\sqrt{147}\)

mà 147>141

nên \(7\sqrt3>\sqrt{141}\)

3: \(\sqrt{\frac{5}{27}}=\sqrt{\frac{5}{9\cdot3}}=\sqrt{\frac{15}{81}}=\frac{\sqrt{15}}{9}\)

\(\sqrt{\frac{11}{64}}=\frac{\sqrt{11}}{\sqrt{64}}=\frac{\sqrt{11}}{8}\)

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

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

Sửa đề: Đưa thừa số vào trong dấu căn

a: \(3\sqrt{x^2}=\sqrt{3^2\cdot x^2}=\sqrt{9x^2}\)

b: \(-5\sqrt{y^4}=-\sqrt{5^2\cdot y^4}=-\sqrt{25y^4}\)

c: \(3\sqrt{5x}=\sqrt{3^2\cdot5x}=\sqrt{45x}\)

d: \(x\sqrt{7}=\sqrt{x^2\cdot7}=\sqrt{7x^2}\)

\(\left(x-5\right)\sqrt{\frac{3}{25-x^2}}=\sqrt{\left(x-5\right)^2}\sqrt{\frac{3}{\left(5-x\right)\left(x+5\right)}}=\sqrt{\left(5-x\right)^2.\frac{3}{\left(5-x\right)\left(x+5\right)}}=\sqrt{\frac{3\left(5-x\right)}{x+5}}\)

thanks 

a: \(3\sqrt{200}=3\cdot10\sqrt{2}=30\sqrt{2}\)

b: \(-5\sqrt{50a^2b^2}=-5\cdot5\sqrt{2a^2b^2}\)

\(=-25\cdot\left|ab\right|\cdot\sqrt{5}\)

c: \(-\sqrt{75a^2b^3}\)

\(=-\sqrt{25a^2b^2\cdot3b}=-5\left|ab\right|\cdot\sqrt{3b}\)