Nature gave us ten fingers, and so it is natural for us to count in tens. Machines count bigger numbers in the same way we do: by counting how many times they run out of digits. This system is called binary and the binary number 10 means the machine ran out of digits one time. A human would call this number two.

The Australian Aboriginal counting system was used together with message sticks sent to neighbouring clans to alert them of, or invite them to, corroborees, set-fights, and ball games. Numbers could clarify the day the meeting was to be held (in a number of “moons”) and where (the number of camps’ distance away).

Square, Cube, Square Root and Cubic Root for Numbers Ranging 0 – 100

A cube number is the answer when an integer is multiplied by itself, then multiplied by itself again. The first five cube numbers are: 1, 8, 27, 64 and 125.

For example, the cube of 3 is 3 x 3 x 3 = 9, and is denoted by 33 = 9. Any natural number raised to the power of three gives the cube of the original number….Cubes 1 to 50 Table.

or more) positive cubes to represent them as a sum. 1, 8, 27, 64, 125, 216, 343, 512. There is a finite set of numbers which cannot be expressed as the sum of distinct positive cubes: 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, (OEIS A001476).

Frequently Asked Questions – FAQs The first ten cube numbers are 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000.

Cube 1 to 100 – Odd Numbers

Step 2: 216 is a perfect cube. Therefore, group the factors of 216 in a pair of three and write in the form of cubes.

Cube Numbers from 1 to 100

Cubes of 1 to 20

A perfect cube is a number that is the cube of an integer. Some other examples of perfect cubes are 1, 8, 27, 64, 125, 216, 343, …

Therefore, the three cube roots of unity are:

• 1, -1/2+i√(3)/2, -1/2 – i√(3)/2.
• 1) One imaginary cube roots of unity is the square of the other.
• 2) If two imaginary cube roots are multiplied then the product we get is equal to 1.
• 3) As there are three cube roots of unity, their sum is zero, let’s see how.

As the cube root of 8000 is a whole number, 8000 is a perfect cube.

Since 2 & 5 do not occur in triplets. ∴ 400 is not a perfect cube.

10

Now, 1000 is a perfect cube. Thus, the required smallest number is 10.

Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.

Is 45 a Perfect Cube? The number 45 on prime factorization gives 3 × 3 × 5. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 45 is irrational, hence 45 is not a perfect cube.

(ii) A perfect cube does not end with two zeros. (iv) There is no perfect cube which ends with 8. (v) The cube of a two digit number may be a three digit number. (vi) The cube of a two digit number may have seven or more digits.

Therefore the cube root of 900 is irrational, hence 900 is not a perfect cube.

Since, 1 3 = 1 , 3 3 = 27 , 5 3 = 125 1^3=1,/ 3^3=27,/ 5^3=125 13=1, 33=27, 53=125…. are all odd. Since a perfect cube ends with three zeroes. e.g. 1 0 3 = 1000 , 2 0 3 = 8000 a n d 3 0 3 = 27000 10^3=1000,/ 20^3=8000/ and/ 30^3=27000 103=1000, 203=8000 and 303=27000….so on.

Hence the smallest number by which 53240 should be divided to make it a perfect cube is 5. The perfect cube in that case is=10648.

Hence the smallest number by which 135 should be divided to make a perfect cube is 5 . Here,the prime factors 3 is not present as triples. Hence, we divide 192 by 3, so that the obtained number becomes a perfect cube.

As the cube root of 729 is a whole number, 729 is a perfect cube.

Question 3 Therefore 81 must be divided by 3 to make it a perfect cube.