问题1.通过质因数分解法找到以下每个数字的立方根。
(i)64
64 = 2 × 2 × 2 × 2 × 2 × 2
By assembling the factors in trio of equal factors, 64 = (2 × 2 × 2) × (2 × 2 × 2)
Therefore, 64 = 2 × 2 = 4
Hence, 4 is cube root of 64.
(ii)512
512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
By assembling the factors in trio of equal factors, 512 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)
Therefore, 512 = 2 × 2 × 2 = 8
Hence, 8 is cube root of 512.
(iii)10648
10648 = 2 × 2 × 2 × 11 × 11 × 11
By assembling the factors in trio of equal factors, 10648 = (2 × 2 × 2) × (11 × 11 × 11)
Therefore, 10648 = 2 × 11 = 22
Hence, 22 is cube root of 10648.
(iv)27000
27000 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 × 5
By assembling the factors in trio of equal factors, 27000 = (2 × 2 × 2) × (3 × 3 × 3) × (5 × 5 × 5)
Therefore, 27000 = (2 × 3 × 5) = 30
Hence, 30 is cube root of 27000.
(v)15625
15625 = 5 × 5 × 5 × 5 × 5 × 5
By assembling the factors in trio of equal factors, 15625 = (5 × 5 × 5) × (5 × 5 × 5)
Therefore, 15625 = (5 × 5) = 25
Hence, 25 is cube root of 15625.
(vi)13824
13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
By assembling the factors in trio of equal factors,
13824 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3)
Therefore, 13824 = (2 × 2 × 2 × 3) = 24
Hence, 24 is cube root of 13824.
(vii)110592
110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3
By assembling the factors in trio of equal factors,
110592 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 ×3)
Therefore, 110592 = (2 × 2 × 2 × 2 × 3) = 48
Hence, 48 is cube root of 110592.
(viii)46656
46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3
By assembling the factors in trio of equal factors,
46656 = (2 × 2 × 2) × (2 × 2 × 2) × (3 × 3 × 3) × (3 × 3 × 3)
Therefore, 46656 = (2 × 2 × 3 × 3) = 36
Hence, 36 is cube root of 46656.
(ix)175616
175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7
By assembling the factors in trio of equal factors,
175616 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2) × (7 × 7 × 7)
Therefore, 175616 = (2 × 2 × 2 × 7) = 56
Hence, 56 is cube root of 175616.
(x)91125
91125 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 5 × 5 × 5
By assembling the factors in trio of equal factors, 91125 = (3 × 3 × 3) × (3 × 3 × 3) × (5 × 5 × 5)
Therefore, 91125 = (3 × 3 × 5) = 45
Hence, 45 is cube root of 91125.
问题。 2.陈述正确或错误。
(i)任何奇数的立方体都是偶数。
False
(ii)完美的立方体不以两个零结尾。
True
(iii)如果数字的平方以5结尾，则其立方以25结尾。
False
(iv)没有以8结尾的完美立方体。
False
(v)两位数字的立方可以是三位数字。
False
(vi)两位数的多维数据集可以具有七个或更多位数字。
False
(vii)一位数字的多维数据集可以是一位数字。
True
问题。 3.有人告诉您1,331是一个完美的立方体。如果不进行因式分解，您能猜出它的立方根是什么?同样，猜出立方根为4913、12167、32768。
(i)1331
Since, the unit digit of cube is 1, the unit digit of cube root 1.
Therefore, we get 1 as unit digit of cube root of 1331.
And the ten’s digit of our cube root is taken as the unit place of the smallest number.
As the unit digit of the cube of a number having digit as unit place 1 is 1.
Therefore,
∛1331 = 11
(ii)4913
Since, the unit digit of cube is 3, the unit digit of cube root will be 7.
Therefore, we get 7 as unit digit of the cube root of 4913. We know 13 = 1 and 23 = 8, 1 > 4 > 8.
So, 1 is taken as ten digits of cube root.
Therefore,
∛4913 = 17
(iii)12167
Since, the unit digit of cube is 7, the unit digit of cube root will be 3.
Therefore, 3 is the unit digit of the cube root of 12167 We know 23 = 8 and 33 = 27, 8 > 12 > 27.
So, 2 is taken as ten digits of cube root.
Therefore,
∛12167 = 23
(iv)32768
Since, the unit digit of cube is 8, the unit digit of cube root will be 2
Therefore, 2 is the unit digit of the cube root of 32768. We know 33 = 27 and 43 = 64, 27 > 32 > 64.
So, 3 is taken as ten digits of cube root.
Therefore,
∛32768 = 32