Bài 1: 

a) \(\sqrt{72}:\sqrt{8}=\sqrt{72:8}=3\)

b) \(\left(\sqrt{28}-\sqrt{7}+\sqrt{112}\right):\sqrt{7}=5\sqrt{7}:\sqrt{7}=5\)

Bài 2: 

a) \(\sqrt{\dfrac{49}{8}}:\sqrt{3\dfrac{1}{8}}=\sqrt{\dfrac{49}{8}:\dfrac{25}{8}}=\sqrt{\dfrac{49}{25}}=\dfrac{7}{5}\)

b) \(\sqrt{54x}:\sqrt{6x}=\sqrt{54x:6x}=\sqrt{9}=3\)

c) \(\sqrt{\dfrac{1}{125}}\cdot\sqrt{\dfrac{32}{35}}:\sqrt{\dfrac{56}{225}}\)

\(=\dfrac{\sqrt{5}}{25}\cdot\dfrac{4\sqrt{2}}{\sqrt{35}}:\dfrac{2\sqrt{14}}{15}\)

\(=\dfrac{\sqrt{5}\cdot4\sqrt{2}\cdot15}{25\cdot\sqrt{35}\cdot\sqrt{14}\cdot2}\)

\(=\dfrac{6}{35}\)

`A=sqrt{3-2sqrt2}-sqrt{3+2sqrt2}`

`=sqrt{2-2sqrt2+1}-sqrt{2+2sqrt2+1}`

`=sqrt{(sqrt2-1)^2}-sqrt{(sqrt2+1)^2}`

`=|sqrt2-1|-|\sqrt2+1|`

`=sqrt2-1-sqrt2-1=-2`

Ta có: \(A=\sqrt{3-2\sqrt{2}}-\sqrt{3+2\sqrt{2}}\)

\(=\sqrt{2}-1-\sqrt{2}-1\)

=-2

a: \(=\sqrt[3]{\dfrac{5}{625}}=\sqrt[3]{\dfrac{1}{125}}=\dfrac{1}{5}\)

b: \(=\sqrt[5]{\left(-\sqrt{5}\right)^5}=-\sqrt{5}\)

Tính:

a,  . +  : 

 7 . 12 + 16 : 8 

   = 84 + 2

    = 86

b, 72 :  - 

 2.6.3-15

= -13

a: \(\sqrt[3]{-125}=\sqrt[3]{\left(-5\right)^3}=-5\)

b: \(\sqrt[4]{\dfrac{1}{81}}=\sqrt[4]{\left(\dfrac{1}{3}\right)^4}=\dfrac{1}{3}\)

a) \(\sqrt[3]{-125}=\sqrt[3]{\left(-5\right)^3}=-5\)

b) \(\sqrt[4]{\dfrac{1}{81}}=\sqrt[4]{\left(\dfrac{1}{3}\right)^4}=\dfrac{1}{3}\)

a) 9
b)90
c)8
d)7/10
e)2/5

a=9

b=90

c=2

d=0,7

e=0,2

\(A=\dfrac{\sqrt{2}-1}{2-1}+\dfrac{\sqrt{3}-\sqrt{2}}{3-2}+...+\dfrac{\sqrt{100}-\sqrt{99}}{100-99}\)

\(=-1+\sqrt{2}-\sqrt{2}+\sqrt{3}-...-\sqrt{99}+\sqrt{100}\)

=10-1

=9

a)2

b)-0,4

c)7

a) \(\sqrt{25-9}\) = \(\sqrt{16}\) = 4

b) \(\sqrt{0,01}-\sqrt{0,25}\) = 0,1 - 0,5 =  -0,4

c)\(\sqrt{2.2^2+4^2}+5^2\) = \(\sqrt{2.4+16+25}\) = \(\sqrt{8+16+25}\) = \(\sqrt{49}\) = 7

a.

\(=\sqrt{\sqrt{5}-2}-\sqrt{5\left(\sqrt{5}+2\right)}+2\sqrt{\sqrt{5}+2}\)

\(=\sqrt{\sqrt{5}-2}-\sqrt{\sqrt{5}+2}\left(\sqrt{5}-2\right)\)

\(=\sqrt{\sqrt{5}-2}-\sqrt{\sqrt{5}-2}\left(\sqrt{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}\right)\)

\(=\sqrt{\sqrt{5}-2}-\sqrt{\sqrt{5}-2}.1=0\)

b.

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

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

\(=\sqrt{\sqrt{2}-1}-\sqrt{\sqrt{2}-1}.\sqrt{\left(\sqrt{2}-1\right)\left(\sqrt{2}+1\right)}\)

\(=\sqrt{\sqrt{2}-1}-\sqrt{\sqrt{2}-1}=0\)

a)

\(M=\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)

\(=\sqrt{4+4\sqrt{5}+5}-\sqrt{4-4\sqrt{5}+5}\)

\(=\sqrt{\left(2+\sqrt{5}\right)^2}-\sqrt{\left(2-\sqrt{5}\right)^2}\)

\(=\left|2+\sqrt{5}\right|-\left|2-\sqrt{5}\right|\)

\(=2+\sqrt{5}-\left(\sqrt{5}-2\right)\) (vì \(2+2\sqrt{5}>0;2-\sqrt{5}< 0\) )

\(=2+\sqrt{5}-\sqrt{5}+2\\ =4\)

b)

\(N=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}\)

\(=\sqrt{7-2\sqrt{7}+1}-\sqrt{7+2\sqrt{7}+1}\)

\(=\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}\)

\(=\left|\sqrt{7}-1\right|-\left|\sqrt{7}+1\right|\)

\(=\sqrt{7}-1-\left(\sqrt{7}+1\right)\) (vì \(\sqrt{7}-1>0;\sqrt{7}+1>0\) )

\(=\sqrt{7}-1-\sqrt{7}-1\\ =-2\)