A cube of a number is the result when that number is multiplied three times. It is written as x3 and read as "x-cubed," "x to the power of 3," or "x raised to 3." For example, if we take the number 5 and multiply it by itself three times, the result is 125, which is called the cube of 5.
Finding the cube root of a number means finding the number that, when cubed, gives us the original number. It is denoted by ∛. Using the same example, the cube root of 125 is 5 and is written as ∛125 = 5.
Cube root is an inverse operation of the cube of a number.
In other words, it is a number that when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3 because 3 multiplied by itself three times equals 27. Cube roots are represented using the symbol ∛, which is called the radical symbol. The cube root of a number can also be expressed using exponents, as x^(1/3) where x is the number whose cube root is being found.
A perfect cube is a whole number that can be obtained by multiplying an integer by itself three times. For instance, 125 is a perfect cube as it can be expressed as 5 × 5 × 5 = 53. Conversely, 121 is not a perfect cube since there is no number that can be multiplied three times to give the product 121. Another term for a perfect cube is a "cube number". The table below lists the perfect cubes of the first 10 natural numbers.
Number/Cube root | Perfect cube |
1 | 1 |
2 | 8 |
3 | 27 |
4 | 64 |
5 | 125 |
6 | 216 |
7 | 343 |
8 | 512 |
9 | 729 |
10 | 1000 |
Here's a step-by-step process to find the cube root of a number.
Step 1: Start with the prime factorization of the given number.
Step 2: Group the prime factors in sets of three starting from the right-most digit.
Step 3: Find the product of the factors in each group.
Step 4: If there are any remaining factors after grouping, write them separately.
Step 5: Take the cube root of each product from step 3.
Step 6: Write down the cube root of each product as a factor.
Step 7: Multiply all the factors obtained from step 6.
This will give you the cube root of the original number. If there are any leftover factors from step 4, then the original number is not a perfect cube, and the cube root will not be a whole number.
For example, let's find the cube root of 64 using the steps above:
Step 1: The number we want to find the cube root of is 64.
Step 2: We could start with 4 as a number that could be the cube root of 64.
Step 3: 4 cubed is 64, which is the same as the original number. So, we have found the cube root of 64, which is 4.
Step 4: To check our answer, we cube 4: 4 x 4 x 4 = 64. So, our answer is correct.
Some people might find the idea of cubes and cube roots intimidating, but actually, there are many cool things to learn about them. You can discover how people used cubes in the past and how cube roots are used in everyday life. Let's explore some fun facts about cubes and cube roots!
1. There are only 10 perfect cubes from 1 to 1000.
2. Cubes of even numbers are even and those of odd numbers are odd
3. The cube of a negative number is always negative.
4. If the digit in one’s place of a number is 0, 1, 4, 5, 6 or 9, then its cube will end in the same digit.
5. If the digit in one’s place of a number is 2, then its cube will end in 8 and vice-versa.
6. If the digit in one’s place of a number is 3, then its cube will end in 7 and vice-versa.
7. Cubes of the numbers ending with the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 end with digits 0, 1, 8, 1, 7, 5, 6, 3, 2, 9 respectively.
8. Here, cubes of numbers ending with digits 0, 1, 4, 5, 6 and 9 end with same digits
A. Its cube is two times the cube of the given number
B. Its cube is three times the cube of the given number
C. Its cube is six times the cube of the given number
D. Its cube is eight times the cube of the given number
A. Cube of a negative number is always positive
B. Cube of a negative number is always negative
C. Cube of a negative number may be positive or negative
D. All of the above
A. 4
B. 5
C. 9
D. 3
A. 28
B. -26
C. -28
D. 7
A. a3 b3
B. a3 / b3
C. ∛a / ∛b
D. ∛a X ∛b
A. 90
B. 300
C. 30
D. 27
Answers:
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