(5 + 6 + 11 - 41) x (1 + 2 + 3 + ... + 100)

= [(5 + 6)  - (11 - 41)] x (1 + 2 +...+ 100)

= [11 - 30 ] x (1 + 2 + ... + 100)

= - 19 x (1 + 2 +...+ 100)

Lớp 5 chưa học số âm.

        12 x 85 + 35 - 182 - 35 x 94

    =  1020 - 35 x (94 - 1) - 182

   = 1020 - 35 x 93 - 182

  = 1020 - 3255 - 182

  = - 2235 - 182

= - 2417

Lớp 5 chưa học số âm 

   2 x 31 x 12 + 4 x 6 + 42 + 8 x 27 x 3

= 24 x 31 + 24 + 42 + 24 x 27

= 24 x (31 + 1 + 27) + 42

= 24 x 59 + 42

= 1458

50) \(\sqrt{98-16\sqrt{3}}=4\sqrt{6}-\sqrt{2}\)

51) \(\sqrt{2-\sqrt{3}}=\dfrac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{3}-1}{\sqrt{2}}=\dfrac{\sqrt{6}-\sqrt{2}}{2}\)

52) \(\sqrt{4+\sqrt{15}}=\dfrac{\sqrt{8+2\sqrt{15}}}{\sqrt{2}}=\dfrac{\sqrt{5}+\sqrt{3}}{\sqrt{2}}=\dfrac{\sqrt{10}+\sqrt{6}}{2}\)

53) \(\sqrt{5-\sqrt{21}}=\dfrac{\sqrt{10-2\sqrt{21}}}{\sqrt{2}}=\dfrac{\sqrt{14}-\sqrt{6}}{2}\)

54) \(\sqrt{6-\sqrt{35}}=\dfrac{\sqrt{12-2\sqrt{35}}}{\sqrt{2}}=\dfrac{\sqrt{14}-\sqrt{10}}{2}\)

55) \(\sqrt{2+\sqrt{3}}=\dfrac{\sqrt{4+2\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{6}+\sqrt{2}}{2}\)

56) \(\sqrt{4-\sqrt{15}}=\dfrac{\sqrt{8-2\sqrt{15}}}{\sqrt{2}}=\dfrac{\sqrt{10}-\sqrt{6}}{2}\)

Can bac 8

7 x 3 = 21    7 x 6 = 42    7 x 5 = 35    7 x 4 = 28

21 : 7 = 3    42 : 7 = 6    35 : 7 = 5    28 : 7 = 4

21 : 3 = 7    42 : 6 = 7    35 : 5 = 7    28 : 4 = 7

7 × 3 = 21      7 × 6 = 42   7 × 5 = 35.     7 × 4 = 28

21 : 7 = 3.     42 : 7 = 6.   35 : 7 = 5.     28 : 7 = 4

21 : 3 = 7.    42 : 6 = 7.   35 : 5 = 7.    28 : 4 = 7

Học sinh nhẩm và ghi kết quả như sau:

35 : 5 = 7

28 : 7 = 4

24 : 6 = 4

21 : 3 = 7

35 : 7 = 5

28 : 4 = 7

24 : 4 = 6

21 : 7 = 3

35 : 5 = 7

28 : 7 = 4

24 : 6 = 4

21 : 3 = 7

35 : 7 = 5

28 : 4 = 7

24 : 4 = 6

21 : 7 = 3

* 4 x 1930 x 3 + 6 x 70 x 2

   = (4 x 3 ) x 1930 +  (6 x 2 ) x 70

   = 12 x 1930 + 12 x 70

   = 12 x (1930 + 70 )

   = 12 x 2000

   = 24000

* 8 x 427 x 3 + 6 x 573 x 4

   = ( 8 x 3 ) x 427 + (6 x 4 ) x 573

   = 24  x 427 + 24 x 573

   = 24 x ( 427 + 573 )

   = 24 x 1000

   = 24000

* 117x (35 + 46 ) - 17 x (35 + 46 )

   = ( 117 - 17 ) x ( 35 + 46 )

   = 100 x 81

   = 8100

câu 1 :24000

câu 2:23 502 168

câu 3: 70 337

câu 1 : (4*3) * 1930 + ( 6*2) *70

= 12 * 1930 + 12* 70 

áp dụng quy tắc nhân một số với 1 tổng ta có

( 1930+70) * 12

=2000* 12

= 24000

\(=\frac{5}{7}\)

\(x=\frac{5}{7}\)

`1)A=sqrt{4+sqrt{10+2sqrt5}}+sqrt{4-sqrt{10+2sqrt5}}`

`<=>A^2=4+sqrt{10+2sqrt5}+4-sqrt{10+2sqrt5}+2sqrt{16-10-2sqrt5}`

`<=>A^2=8+2sqrt{6-2sqrt5}`

`<=>A^2=8+2sqrt{(sqrt5-1)^2}`

`<=>A^2=8+2(sqrt5-1)`

`<=>A^2=6+2sqrt5=(sqrt5+1)^2`

`<=>A=sqrt5+1(do \ A>0)`

`b)B=sqrt{35+12sqrt6}-sqrt{35-12sqrt6}`

Vì `35+12sqrt6>35-12sqrt6`

`=>B>0`

`B^2=35+12sqrt6+35-12sqrt6-2sqrt{35^2-(12sqrt6)^2}`

`<=>B^2=70-2sqrt{361}`

`<=>B^2=70-2sqrt{19^2}=70-38=32`

`<=>B=sqrt{32}=4sqrt2(do \ B>0)`

`3)(4+sqrt{15})(sqrt{10}-sqrt6)sqrt{4-sqrt{15}}`

`=sqrt{4+sqrt{15}}.sqrt{4-sqrt{15}}.sqrt{4+sqrt{15}}(sqrt{10}-sqrt6)`

`=sqrt{16-15}.sqrt2(sqrt5-sqrt3).sqrt{4+sqrt{15}}`

`=sqrt{8+2sqrt{15}}(sqrt5-sqrt3)`

`=sqrt{5+2sqrt{5.3}+3}(sqrt5-sqrt3)`

`=sqrt{(sqrt5+sqrt3)^2}(sqrt5-sqrt3)`

`=(sqrt5+sqrt3)(sqrt5-sqrt3)`

`=5-3=2`

a: =>x=3/7+3/5=15/35+21/35=36/35

b: =>x/35=4/5-5/7=28/35-25/35=3/35

=>x=3

c: =>x<3/4+8/4=11/4

=>\(x\in\left\{0;1;2;3\right\}\)

d: =>5/3<x<5/6+24/6=29/6

=>\(x\in\left\{2;3;4\right\}\)

e: =>x<10/12-9/12=1/12

=>x=0

f: =>2/3<x<12/6-5/6=7/6

=>x=1

\(\dfrac{3}{5}+\dfrac{2}{3}=\dfrac{9}{15}+\dfrac{10}{15}=\dfrac{19}{15}\\ \dfrac{5}{7}-\dfrac{1}{2}=\dfrac{10}{14}-\dfrac{7}{14}=\dfrac{3}{14}\\ \dfrac{5}{6}\times\dfrac{4}{5}=\dfrac{1}{3}\times\dfrac{2}{1}=\dfrac{2}{3}\\ \dfrac{7}{9}:\dfrac{4}{3}=\dfrac{7}{9}\times\dfrac{3}{4}=\dfrac{7}{12}\)

\(\dfrac{3}{5}+\dfrac{2}{3}=\dfrac{9}{15}+\dfrac{10}{15}=\dfrac{19}{15}\)

\(\dfrac{5}{7}-\dfrac{1}{2}=\dfrac{10}{14}-\dfrac{7}{14}=\dfrac{3}{14}\)

\(\dfrac{5}{6}\text{×}\dfrac{4}{5}=\dfrac{5\text{×}4}{6\text{×}5}=\dfrac{2}{3}\)

\(\dfrac{7}{9}:\dfrac{4}{3}=\dfrac{7}{9}\text{×}\dfrac{3}{4}=\dfrac{7\text{×}3}{9\text{×}4}=\dfrac{7\text{×}3}{3\text{×}3\text{×}4}=\dfrac{7}{12}\)

\(\dfrac{3}{5}+\dfrac{2}{3}=\dfrac{9}{15}+\dfrac{10}{15} = \dfrac{19}{15}\)

\(\dfrac{5}{7}-\dfrac{1}{2}=\dfrac{10}{14}-\dfrac{7}{14}=\dfrac{3}{14}\)

\(\dfrac{5}{6} \times \dfrac{4}{5} = \dfrac{4}{6}= \dfrac{2}{3}\)

\( \dfrac{7}{9} : \dfrac{4}{3} = \dfrac{7}{9} \times \dfrac{3}{4} = \dfrac{7}{12}\)

12) \(\sqrt{15-6\sqrt{6}}+\sqrt{35-12\sqrt{6}}\)

\(=3-\sqrt{6}+3\sqrt{3}-2\sqrt{2}\)

13) \(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

\(=3\sqrt{5}-1-2\sqrt{5}+3\)

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