1) \(\sqrt{21+12\sqrt{3}}=\sqrt{3^2+2.3.2\sqrt{3}+\left(2\sqrt{3}\right)^2}=\sqrt{\left(3+2\sqrt{3}\right)^2}\)

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

2) \(\sqrt{57-40\sqrt{2}}=\sqrt{5^2-2.5.4\sqrt{2}+\left(4\sqrt{2}\right)^2}=\sqrt{\left(5-4\sqrt{2}\right)^2}\)

                                                                           \(=\left|5-4\sqrt{2}\right|=4\sqrt{2}-5\)

3) \(\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\)

\(=\left|\sqrt{5}+1\right|+\left|\sqrt{5}-1\right|\)

\(=\sqrt{5}+1+\sqrt{5}-1\)

\(=2\sqrt{5}\)

a) −512−512 . 419419 +−712−712 . 419419 -40574057 Đầu tiên, chúng ta tính toán phép nhân: −512 x 419419 = -214,748,928 −712 x 419419 = -298,238,328

Tiếp theo, chúng ta tính tổng của hai kết quả: -214,748,928 + -298,238,328 = -513,987,256

Cuối cùng, chúng ta trừ đi 40574057: -513,987,256 - 40574057 = -554,561,313

Vậy kết quả của phép tính a là -554,561,313.

b) 1313 . 4545 + 1313.1.1515 + ( −32−32 )^2 Đầu tiên, chúng ta tính toán phép nhân: 1313 x 4545 = 5,964,385 1313 x 1.1515 = 1,511.195 −32 x −32 = 1,024

Tiếp theo, chúng ta tính tổng của ba kết quả: 5,964,385 + 1,511.195 + 1,024 = 5,966,920.195

Vậy kết quả của phép tính b là 5,966,920.195.

\(=-10\)

\(=-6\)

Bài 1: 

\(A=\dfrac{-1}{3}+1+\dfrac{1}{3}=1\)

\(B=\dfrac{2}{15}+\dfrac{5}{9}-\dfrac{6}{9}=\dfrac{2}{15}-\dfrac{1}{9}=\dfrac{18-15}{135}=\dfrac{3}{135}=\dfrac{1}{45}\)

\(C=\dfrac{-1}{5}+\dfrac{1}{4}-\dfrac{3}{4}=\dfrac{-1}{5}-\dfrac{1}{2}=\dfrac{-7}{10}\)

Bài 2: 

a: \(=\dfrac{1}{5}+\dfrac{1}{2}+\dfrac{2}{5}-\dfrac{3}{5}+\dfrac{2}{21}-\dfrac{10}{21}+\dfrac{3}{20}\)

\(=\left(\dfrac{1}{5}+\dfrac{2}{5}-\dfrac{3}{5}\right)+\left(\dfrac{2}{21}-\dfrac{10}{21}\right)+\left(\dfrac{1}{2}+\dfrac{3}{20}\right)\)

\(=\dfrac{-8}{21}+\dfrac{13}{20}=\dfrac{113}{420}\)

b: \(B=\dfrac{21}{23}-\dfrac{21}{23}+\dfrac{125}{93}-\dfrac{125}{143}=\dfrac{6250}{13299}\)

Bài 3:

\(\dfrac{7}{3}-\dfrac{1}{2}-\left(-\dfrac{3}{70}\right)=\dfrac{7}{3}-\dfrac{1}{2}+\dfrac{3}{70}=\dfrac{490}{210}-\dfrac{105}{210}+\dfrac{9}{210}=\dfrac{394}{210}=\dfrac{197}{105}\)

\(\dfrac{5}{12}-\dfrac{3}{-16}+\dfrac{3}{4}=\dfrac{5}{12}+\dfrac{3}{16}+\dfrac{3}{4}=\dfrac{20}{48}+\dfrac{9}{48}+\dfrac{36}{48}=\dfrac{65}{48}\)

Bài 4:

 \(\dfrac{3}{4}-x=1\)

\(\Rightarrow-x=1-\dfrac{3}{4}\)

\(\Rightarrow x=-\dfrac{1}{4}\)

Vậy: \(x=-\dfrac{1}{4}\)

\(x+4=\dfrac{1}{5}\)

\(\Rightarrow x=\dfrac{1}{5}-4\)

\(\Rightarrow x=-\dfrac{19}{5}\)

Vậy: \(x=-\dfrac{19}{5}\)

\(x-\dfrac{1}{5}=2\)

\(\Rightarrow x=2+\dfrac{1}{5}\)

\(\Rightarrow x=\dfrac{11}{5}\)

Vậy: \(x=\dfrac{11}{5}\)

\(x+\dfrac{5}{3}=\dfrac{1}{81}\)

\(\Rightarrow x=\dfrac{1}{81}-\dfrac{5}{3}\)

\(\Rightarrow x=-\dfrac{134}{81}\)

Vậy: \(x=-\dfrac{134}{81}\)

a) \(E=\sqrt{\left|12\sqrt{5}-29\right|}-\sqrt{12\sqrt{5}+29}\)

\(\Leftrightarrow E^2=\left|12\sqrt{5}-29\right|-12\sqrt{5}-29\)

\(\Leftrightarrow E^2=29-12\sqrt{5}-12\sqrt{5}-29\)

\(\Leftrightarrow E^2=-24\sqrt{5}\)

\(\Leftrightarrow E=-2\sqrt{6\sqrt{5}}\)

b) Đặt \(F=\sqrt{\left|40\sqrt{2}-57\right|}-\sqrt{40\sqrt{2}+57}\)

\(\Leftrightarrow F^2=\left|40\sqrt{2}-57\right|-40\sqrt{2}-57\)

\(\Leftrightarrow F^2=57-40\sqrt{2}-40\sqrt{2}-57\)

\(\Leftrightarrow F^2=-80\sqrt{2}\)

\(\Leftrightarrow F=-4\sqrt{5\sqrt{2}}\)

Giải:

1) \(\sqrt{21+12\sqrt{3}}\)

\(=\sqrt{12+9+12\sqrt{3}}\)

\(=\sqrt{12+12\sqrt{3}+9}\)

\(=\sqrt{\left(2\sqrt{3}\right)^2+2.2\sqrt{3}.3+3^2}\)

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

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

Vậy ...

2) \(\sqrt{57-40\sqrt{2}}\)

\(=\sqrt{32+25-40\sqrt{2}}\)

\(=\sqrt{32-40\sqrt{2}+25}\)

\(=\sqrt{\left(4\sqrt{2}\right)^2-2.4\sqrt{2}.5+5^2}\)

\(=\sqrt{\left(4\sqrt{2}-5\right)^2}\)

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

Vậy ...

3) \(\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\)

\(=\sqrt{5}+1+\sqrt{5}-1\)

\(=2\sqrt{5}\)

Vậy ...

b: \(B=\dfrac{5}{2}-\dfrac{7}{2}+\dfrac{3}{8}+\dfrac{6}{8}+\dfrac{-6}{11}-\dfrac{5}{11}=-2-1+\dfrac{9}{8}=\dfrac{9}{8}-3=-\dfrac{15}{8}\)

c: \(C=\left(\dfrac{4}{3}+\dfrac{7}{3}+\dfrac{1}{3}\right)+\left(\dfrac{2}{5}+\dfrac{3}{5}\right)=4+1=5\)

d: \(D=\dfrac{4}{19}\left(\dfrac{-5}{6}-\dfrac{7}{12}\right)-\dfrac{40}{57}\)

\(=\dfrac{4}{19}\cdot\dfrac{-17}{12}-\dfrac{40}{57}=-1\)

e: \(E=\dfrac{1}{3}\left(\dfrac{4}{5}-\dfrac{9}{5}\right)+\dfrac{2}{3}=\dfrac{2}{3}-\dfrac{1}{3}=\dfrac{1}{3}\)

câu 1) 

\(\dfrac{-12}{18}+\left(\dfrac{-21}{35}\right)=\dfrac{-19}{15}\)
câu 2) 

\(-\dfrac{3}{21}+\dfrac{6}{42}=0\)
câu 3)

\(-\dfrac{18}{24}+\dfrac{15}{21}=-\dfrac{1}{28}\)
câu 4) 

\(\dfrac{1}{6}+\dfrac{2}{5}=\dfrac{17}{30}\)
câu 5) 

\(\dfrac{3}{5}+\left(-\dfrac{7}{4}\right)=-\dfrac{23}{20}\)
câu 6) 

\(\left(-2\right)+\left(\dfrac{-5}{8}\right)=\dfrac{-21}{8}\)
câu 7) 

\(\dfrac{1}{-8}+\left(-\dfrac{5}{9}\right)=-\dfrac{49}{72}\)
câu 8) 

\(\dfrac{4}{13}+\dfrac{12}{39}=\dfrac{8}{13}\)
câu 9) 

\(\dfrac{1}{21}+\dfrac{1}{28}=\dfrac{1}{12}\)
câu 10) 

\(-\dfrac{3}{29}+\dfrac{16}{58}=\dfrac{5}{29}\)
câu 11) 

\(\dfrac{8}{40}+\left(-\dfrac{36}{45}\right)=-\dfrac{3}{5}\)
câu 12) 

\(-\dfrac{8}{18}+\left(-\dfrac{15}{27}\right)=-1\)
câu 13) 

\(\dfrac{13}{30}+\left(-\dfrac{1}{5}\right)=\dfrac{7}{30}\)
câu 14) 

\(\dfrac{2}{21}+\dfrac{1}{28}=\dfrac{11}{84}\)
câu 15) 

\(5+\left(-\dfrac{3}{4}\right)=\dfrac{17}{4}\)
câu 16) 

\(\dfrac{18}{24}+\dfrac{45}{-10}=-\dfrac{15}{4}\)

c) Ta có: \(\dfrac{3}{5}+\dfrac{-5}{20}+\dfrac{30}{75}+\dfrac{-7}{4}\)

\(=\dfrac{3}{5}+\dfrac{2}{5}+\dfrac{-1}{4}+\dfrac{-7}{4}\)

\(=1-2=-1\)

Giải:

a)-1/12+4/3=-1/12+16/12=15/12=5/4

b)(-4/14-3/15)-(1/5-20/35-(-1)).7

=-17/35-22/35.7

=-17/35-22/5

=-171/35

c)3/5+-5/20+30/75+-7/4

=3/5+-1/4+2/5+-7/4

=(3/5+2/5)+(-1/4+-7/4)

=1+-2

=-1

d)5/6.-12/14+7/13

=-5/7+7/13

=-16/91

e)2/-9-5/-36-1/4

=-1/12-1/4

=-1/3

f)2/23+-5/12+7/18+21/23+-7/12

=(2/23+21/23)+(-5/12+-7/12)+7/18

=1+-1+7/18

=7/18