Lời giải:

a) $\sqrt{96.125}=\sqrt{96}.\sqrt{125}=\sqrt{4^2.6}.\sqrt{5^2.5}$

$=4\sqrt{6}.5\sqrt{5}=20\sqrt{30}$

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

c,d) Biểu thức không có căn.

\(\sqrt{5a^2}=\left|\sqrt{5}a\right|,vìa\le0\Rightarrow\left|a\right|=-a\Rightarrow\left|\sqrt{5a}\right|=-\sqrt{5}a\)

\(\sqrt{34+24\sqrt{2}}\)

\(=\sqrt{18+2.12\sqrt{2}+16}\)

\(=\sqrt{\left(3\sqrt{2}+4\right)^2}\)

\(=3\sqrt{2}+4\)

a: \(=\sqrt{2^5\cdot3\cdot5^3}=2^2\cdot5\cdot\sqrt{2\cdot3\cdot5}=20\sqrt{30}\)

b: \(=a^2b^2\sqrt{b}\)

Giải:

a) \(\sqrt{a^4.\left(3-a\right)^2}\)

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

\(=\left|a^2\left(3-a\right)\right|\)

b) \(\sqrt{27.48.\left(a-3\right)^2}\)

\(=\sqrt{3.9.16.3.\left(a-3\right)^2}\)

\(=\sqrt{3.3.9.16\left(a-3\right)^2}\)

\(=\sqrt{\left(9.4\left(a-3\right)\right)^2}\)

\(=\left|9.4\left(a-3\right)\right|\)

\(=\left|36\left(a-3\right)\right|\)

c) \(\sqrt{48.75a^2}\)

\(=\sqrt{16.3.25.3a^2}\)

\(=\sqrt{\left(4.3.5a\right)^2}\)

\(=\left|4.3.5a\right|\)

\(=\left|60a\right|\)

d) \(\sqrt{2^4.\left(-9\right)^2}\)

\(=\sqrt{2^4.9^2}\)

\(=\sqrt{\left(2^2.9\right)^2}\)

\(=\left|2^2.9\right|\)

\(=\left|36\right|=36\)

Vậy ...

Bài 1: 

\(\sqrt{27a^2}=3a\sqrt{3}\)

Bài 2: 

\(\dfrac{2}{3}\sqrt{3xy}=\sqrt{3xy\cdot\dfrac{4}{9}}=\sqrt{\dfrac{4}{3}xy}\)

Bài 3: 

\(=4\sqrt{b}+2\cdot2\sqrt{10b}-3\cdot3\sqrt{10b}=4\sqrt{b}-5\sqrt{10b}\)