\(\sqrt{2-\sqrt{3}}\left(\sqrt{6}+\sqrt{2}\right)=\sqrt{4-2\sqrt{3}}\left(\sqrt{3}+1\right)=\sqrt{\left(\sqrt{3}-1\right)^2}\left(\sqrt{3}+1\right)\)

\(=\left|\sqrt{3}-1\right|\left(\sqrt{3}+1\right)=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)=3-1=2\)

\(\dfrac{x-25}{\sqrt{x}-5}-\dfrac{x+4\sqrt{x}+4}{\sqrt{x}+2}=\dfrac{\left(\sqrt{x}-5\right)\left(\sqrt{x}+5\right)}{\sqrt{x}-5}-\dfrac{\left(\sqrt{x}+2\right)^2}{\sqrt{x}+2}\)

\(=\sqrt{x}+5-\left(\sqrt{x}+2\right)=5-2=3\)

a: Ta có: \(\sqrt{2-\sqrt{3}}\cdot\left(\sqrt{6}+\sqrt{2}\right)\)

\(=\sqrt{4-2\sqrt{3}}\cdot\left(\sqrt{3}+1\right)\)

\(=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)\)

=3-1

=2

b: Ta có: \(\dfrac{x-25}{\sqrt{x}-5}-\dfrac{x+4\sqrt{x}+4}{\sqrt{x}+2}\)

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

=3

A = (-25).8.2.5.(-4).13 = [(-25).(-4)].8.2.5.13 = 100.8.10.13 = 10400

B = 13.(-7) + (-13).57 + 13.(-36) = 13.(-7) - 13.57 + 13.(-36)

                                                      = 13.[(-7) + (-57) + (-36)]

                                                      = 13. (-100)

                                                      = -1300

Ta có: \(A=\left(-25\right)\cdot8\cdot2\cdot5\cdot\left(-4\right)\cdot13\)

\(=\left[\left(-25\right)\cdot\left(-4\right)\right]\cdot\left(2\cdot5\right)\cdot\left(8\cdot13\right)\)

\(=104000\)

Ta có: \(B=13\cdot\left(-7\right)+\left(-13\right)\cdot57+13\cdot\left(-36\right)\)

\(=13\cdot\left(-7\right)-13\cdot57-13\cdot36\)

\(=13\left(-7-57-36\right)\)

\(=13\cdot\left(-100\right)=-1300\)

a/ A= 119+(-213)+212+(-118)+2009

A= ! - 1 + 2009

A= 2009

b/ B=223+132+187-23-32-87

B = 200 + 100 + 100

B = 400

c/ C= -2012+(-596)+(-201)+496+301

C = -2012 - 100 + 100

C = -2012

 d/ D= -329+(15-101)-(25-440)

D = 0

hok tốt!!!

\(a,A=119+\left(-213\right)+212+\left(-118\right)+2009\)

\(A=\left(119+212+2009\right)+\left[\left(-213\right)+\left(-118\right)\right]\)

\(A=2340+\left(-331\right)\)

\(A=2009\)

\(b,B=223+132+187-23-32-87\)

\(B=\left(223+132+187\right)+\left(-23-32-87\right)\)

\(B=542-142\)

\(B=400\)

A. 3,242 + 2,326 + 192 = 5,760

B. 520,401 + 27,429 - 13,965 = 534,865

C. 13,228 - (28,073 - 16,785) = 2,940

D. 86,572 - (58,406 + 9,275) = 18,891

a: \(3242+2326+192\)

\(=3242+192+2326\)

\(=3434+2326=5760\)

b: \(520401+27429-13965\)

\(=\left(520401+27429\right)-13965\)

\(=547830-13965=533865\)

c: \(13228-\left(28073-16785\right)\)

\(=13228+16785-28073\)

\(=\left(13228+16785\right)-28073\)

\(=30013-28073=1940\)

d: \(86572-\left(58406+9275\right)\)

\(=86572-67681\)

=18891

a. 1/3 + 1/4 - 1/6

= 7/12 - 1/6

= 5/12

b. 2/5 x 5/7 : 3/4

= 2/7 : 3/4

= 8/21

a: \(123,15-23,15\cdot4\)

\(=100+23,15-23,15\cdot4\)

\(=100-23,15\cdot3\)

\(=100-69,45=30,55\)

b: \(18,64-8,64:\left(12,2+12,8\right)\)

\(=18,64-8,64:25\)

\(=18,64-8,64\cdot0,04\)

\(=10+8,64-8,64\cdot0,04\)

\(=10+8,64\cdot0,96=10+8,2944=18,2944\)

nhanh chưa

a) 21/20 : 4/5

= 21/16

b) x = 8/7+3/9

    x = 31/21

a) \(\dfrac{1}{3}+\dfrac{4}{3}\times\dfrac{1}{2}=\dfrac{1}{3}+\dfrac{4}{6}=\dfrac{1}{3}+\dfrac{2}{3}=\dfrac{3}{3}=1\)

b) \(\dfrac{3}{5}\times\dfrac{4}{7}:\dfrac{16}{21}=\dfrac{3}{5}\times\dfrac{4}{7}\times\dfrac{21}{16}=\dfrac{12}{35}\times\dfrac{21}{16}=\dfrac{252}{560}=\dfrac{9}{20}\)

\(1,\\ a,2< 3\Rightarrow2^{30}< 3^{30}\Rightarrow-2^{30}>-3^{30}\\ b,6^{10}=6^{2\cdot5}=\left(6^2\right)^5=36^5>35^5\left(36>35\right)\)

\(2,\\ a,\dfrac{\left(-3\right)^{10}\cdot15^5}{25^3\cdot\left(-9\right)^7}=\dfrac{3^{10}\cdot5^5\cdot3^5}{5^6\cdot3^{14}}=\dfrac{3}{5}\\ b,\left(8x-1\right)^{2x+1}=5^{2x+1}\\ \Leftrightarrow8x-1=5\\ \Leftrightarrow x=\dfrac{3}{4}\)

Bài 2: 

a: Ta có: \(\dfrac{\left(-3\right)^{10}\cdot15^5}{25^3\cdot\left(-9\right)^7}\)

\(=\dfrac{-3^{10}\cdot3^5\cdot5^5}{5^6\cdot3^{14}}\)

\(=-\dfrac{3}{5}\)

b: Ta có: \(\left(8x-1\right)^{2x+1}=5^{2x+1}\)

\(\Leftrightarrow8x-1=5\)

\(\Leftrightarrow8x=6\)

hay \(x=\dfrac{3}{4}\)

Bài 1: 

a: \(-2^{30}=-8^{10}\)

\(-3^{30}=-27^{10}\)

mà 8<27

nên \(-2^{30}>-3^{30}\)

b: \(35^5=35^5\)

\(6^{10}=36^5\)

mà 35<36

nên \(35^5< 6^{10}\)