Các dạng bài tập căn bậc ba chọn lọc

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CĂN BẬC BA

  • Căn bậc ba của một số a là số x sao cho x cubed equals a. 
  • Mọi số a đều có duy nhất một căn bậc ba.
  • A less than B left right double arrow cube root of A less than cube root of B
  • cube root of A. B end root equals cube root of A. cube root of B
  • Với B not equal to 0 ta có: cube root of A over B end root equals fraction numerator cube root of A over denominator cube root of B end fraction 

DẠNG 1: THỰC HIỆN PHÉP TÍNH

Phương pháp: Áp dụng công thức:

cube root of a cubed end root equals a semicolon open parentheses cube root of a close parentheses cubed equals a 

và các hằng đẳng thức:

open parentheses a plus b close parentheses cubedequals a cubed plus 3 a squared b plus 3 a b squared plus b cubed comma open parentheses a minus b close parentheses cubedequals a cubed minus 3 a squared b plus 3 a b squared minus b cubed                                 

  a cubed plus b cubedequals open parentheses a plus b close parentheses open parentheses a squared minus a b plus b squared close parentheses commaa cubed minus b cubedequals open parentheses a minus b close parentheses open parentheses a squared plus a b plus b squared close parentheses 

Câu 1: Thực hiện phép tính:

a)cube root of 216

b)cube root of 729

c)cube root of 1331 

d)cube root of negative 343 end root

e)cube root of negative 1728 end root

f)cube root of 8 over 27 end root  

Bài 2: Thực hiện các phép tính sau:

a)cube root of open parentheses square root of 2 plus 1 close parentheses open parentheses 3 plus 2 square root of 2 close parentheses end root

b)cube root of open parentheses 4 minus 2 square root of 3 close parentheses open parentheses square root of 3 minus 1 close parentheses end root

c)cube root of negative 64 end root minus cube root of 125 plus cube root of 216 

d)open parentheses cube root of 4 plus 1 close parentheses cubed minus open parentheses cube root of 4 minus 1 close parentheses cubed

e)open parentheses cube root of 9 minus cube root of 6 plus cube root of 4 close parentheses open parentheses cube root of 3 plus cube root of 2 close parentheses  

Bài 3: Thực hiện các phép tính sau:

a)A equals cube root of 2 plus square root of 5 end root plus cube root of 2 minus square root of 5 end root

b)B equals cube root of 9 plus 4 square root of 5 end root plus cube root of 9 minus 4 square root of 5 end root

c)C equals open parentheses 2 minus square root of 3 close parentheses. cube root of 26 plus 15 square root of 3 end root

d)D equals cube root of 3 plus square root of 9 plus 125 over 27 end root end rootnegative cube root of negative 3 plus square root of 9 plus 125 over 27 end root end root  

Bài 4: Cho cube root of 16 plus cube root of negative 54 end root plus cube root of 128 equals cube root of 2. a. Tính a

Bài 5: Cho a cubed equals 5. cube root of 2 minus 1 minus 3. cube root of 4. Tính a

Bài 6: Biết square root of open parentheses 1 plus square root of 3 close parentheses squared end root plus square root of open parentheses 1 minus square root of 3 close parentheses squared end root equals x plus y square root of 3 với x, y là các số nguyên. Tính x space plus space y 

Bài 7: Tính giá trị biểu thức

 A equals open parentheses 3 x cubed plus 8 x squared plus 2 close parentheses to the power of 2009negative 3 to the power of 2009  

biết  x equals fraction numerator open parentheses square root of 5 plus 2 close parentheses cubed square root of 17 square root of 5 minus 38 end root over denominator square root of 5 plus square root of 14 minus 6 square root of 5 end root end fraction

Bài 8: Tính:  

A equals fraction numerator cube root of 4 plus cube root of 2 plus 2 over denominator cube root of 4 plus cube root of 2 plus 1 end fraction semicolon

B equals square root of 3 plus square root of 3 plus cube root of 10 plus 6 square root of 3 end root end root semicolon

C equals fraction numerator 4 plus 2 square root of 3 over denominator cube root of 10 plus 6 square root of 3 end root end fraction

Bài 9: Tính:

A equals cube root of 1 plus 2 square root of 6 end root minus
root index 6 of 25 plus 4 square root of 6 end root. cube root of 2 square root of 6 minus 1 end root plus 1 

Bài 10: Tính:

 A equals fraction numerator cube root of 7 plus 2 square root of 5 end root over denominator square root of 4 plus 2 square root of 3 end root minus square root of 3 end fraction

Bài 11: Chứng minh rằng:

fraction numerator square root of open parentheses fraction numerator 9 minus 2 square root of 3 over denominator square root of 3 minus cube root of 2 end fraction plus 3 cube root of 2 close parentheses. square root of 3 end root over denominator 3 plus root index 6 of 108 end fractionequals cube root of square root of 5 plus 2 end root minus cube root of square root of 5 minus 2 end root

PHƯƠNG TRÌNH QUY VỀ PHƯƠNG TRÌNH BẬC HAI

Bài 12: Tính:

a) cube root of 2 minus square root of 5 end root. root index 6 of 9 plus 4 square root of 5 end root plus cube root of 2 plus square root of 5 end root                           

b) fourth root of 17 plus 12 square root of 2 end root minus square root of 2 

c) fourth root of 56 minus 24 square root of 5 end root                                           

d) fourth root of 28 minus 16 square root of 3 end root plus 1 

e) cube root of 7 plus 5 square root of 2 end root plus cube root of 7 minus 5 square root of 2 end root 

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