\(\frac{\sqrt{a^3+2a^2b}+\sqrt{a^4+2a^3b}-\sqrt{a^3}-a^2b}{\sqrt{\left(2a+b-\sqrt{a^2+2ab}\right)}.\left(\sqrt[3]{a^2}-\sqrt[6]{a^5}+a\right)}\)

Cho a,b > 0. Hãy đơn giản biểu thức :

\(T=\frac{\sqrt{a^3+2a^2b}+\sqrt{a^4+2a^3b}-\sqrt{a^3}-a^2b}{\sqrt{\left(2a+b-\sqrt{a^2+2ab}\right)}.\left(\sqrt[3]{a^2}-\sqrt[6]{a^5}+a\right)}\)

cho a, b >0. hãy đơn giản biểu thức       \(\frac{\sqrt{a^{3^{ }}+2a^2b}+\sqrt{a^4+2ab}-\sqrt{a^3}-a^2b}{\sqrt{\left(2a+b-\sqrt{a^2+2ab}\right)}.\left(\sqrt[3]{a^2}-\sqrt[6]{a^5}+a\right)}\)

cho a,b > 0. Hãy đơn giản biểu thức:

\(T=\frac{\sqrt{a^3+2a^2b}+\sqrt{a^4+2a^3b}-\sqrt{a^3}-a^2b}{\sqrt{\left(2a+b-\sqrt{a^2+2ab}\right)}.\left(\sqrt[3]{a^2}-\sqrt[6]{a^5}+a\right)}\)

cho a,b,c >0 hãy đơn giản bt :

A=\(\frac{\sqrt{a^3+2a^2b}+\sqrt{a^4+2a^3b}-\sqrt{a^3}-a^2b}{\sqrt{2a+b-\sqrt{a^2+2ab}}.\left(\sqrt[3]{a^2}-\sqrt[6]{a^5}+a\right)}\)

Cho 

\(\sqrt{a}+\sqrt{b}+\sqrt{c}=\sqrt{3}\)

\(\sqrt{\left(a+2b\right)\left(a+2c\right)}+\sqrt{\left(b+2a\right)\left(b+2c\right)}+\sqrt{\left(c+2a\right)\left(c+2b\right)}=3\)

Hãy tính \(\left(2\sqrt{a}+3\sqrt{b}-4\sqrt{c}\right)^2\)

cho a,b,c dương và a+b+c=1.CMR: \(\frac{\sqrt{\left(^{a^2+2ab}\right)}}{\sqrt{\left(b^2+2c^2\right)}}+\frac{\sqrt{\left(^{b^2+2bc}\right)}}{\sqrt{\left(c^2+2a^2\right)}}+\frac{\sqrt{\left(^{c^2+2ac}\right)}}{\sqrt{\left(a^2+2b^2\right)}}\ge\frac{1}{a^2+b^2+c^2}\)

cho \(\sqrt{a}+\sqrt{\sqrt{b}+}\sqrt{c}=\sqrt{3}va\sqrt{\left(a+2b\right)\left(a+2c\right)}+\sqrt{\left(b+2a\right)\left(b+2c\right)}+\sqrt{\left(c+2a\right)\left(c+2b\right)}=3\)

tính M=\(\left(2\sqrt{a}+3\sqrt{b}-4\sqrt{c}\right)^2\)

1. Rút gọn

a) \(\sqrt{\left(a^2+b^2-2ab\right)\left(a^4+b^2-2a^2b\right)}\)

b)\(\dfrac{ab+2\sqrt{b}}{3\sqrt{b}}:\dfrac{3\sqrt{b}}{ab-2\sqrt{b}}\)