Cubes from 1 to 50

Cubes from 1 to 50 can be remembered by using some formulas and tricks to solve them. We will also discuss the cube root of the number formula and how to find cube roots of big numbers. But prior to that, it is important to know the basics about what a cube of a number is and how it can be used and what are cube roots. Obviously, cubes of the first 10 or 15 are easy to learn but the problem is with big numbers. Don’t worry here we will look at some formulas on how to find the cube root of big numbers. Cubes also play an important role at each level in mathematics. Whether you’re in school or college the knowledge of cubes is necessary because it makes calculation easier.

What is a cube of a number?

If you want to determine the cube of a number, multiply it by itself first, then multiply the result of that multiplied by the original number once again. Let’s go through the same procedure to determine the cube of seven. We already know that the cube of a number N equals N N N. But what about the square of a number N? As a result, the cube of seven is 7 x 7 x 7. Then, in order to determine the cube of seven, we must first discover the value of seven times seven. The value of this variable is 49. We will now discover 49 7 as a result of our search. This is equivalent to the number 343. The cube of number 7 is 343 as a result of this calculation.

It can be represented in a particular manner that is (a)3. Here, a is any number, and 3 is the power of that number or we can pronounce it as the cube of a is. Let’s take a few examples of numbers between 1 to 50.

13 = 1*1*1 = 1

23= 2*2*2 = 4*2 = 8

33= 3*3*3 = 9*3 = 27

43= 4*4*4 = 16*4 = 64

So, till 10 we can easily find the cubes.

You can write it in word form also. For example,

Cube of 5 is 5*5*5 = 125

Cube of 6 is 6*6*6 = 36*6 = 216

Cube of 7 is 343

Cube of 8 is 512

Cube of 9 is 729

Cube of 10 is 1000

But the difficulty is after 10. So, here is one cube root of number formula that can be applied for such numbers

(a+b)^{3 = a3 + 3a2b + 3ab2 + b3}

You can read it as

a + b whole cube is equal to a cube plus 3a square b plus 3ab squared plus b cube.

Let’s take some examples

113

First, we will break 11 into two numbers whose cubes are known. Consider 5 and 6. Now, apply the above formula

(a+b)³ = a³ + 3a2b + 3ab^{2 + b3}

Here: a=5 and b=6

(5+6)³ = 53 + 3(5)²(6) + 3(5)(6)² + 63

              = 125 + 75*6 + 15*36 + 216

              = 125+450+540+216

After adding all the terms

11³ = 1331

Like this, you can find for other numbers but this formula can also work only for those numbers which can split into two single-digit numbers which can include the numbers till 20

Cubes of 12 to 20 are (by using formula)

12³ = 1728

13³ = 2197

14³ = 2744

15³ = 3375

16³ = 4096

17³ = 4913

18³ = 5832

19³ = 6859

20³ = 8000

These are the cubes of remaining numbers from 21 to 50.

22² = 10684                                  36²= 46656

23²= 12167                                  37²= 50653

24²= 13824                                  382= 54872

252= 15625                                 39²= 59319

26²= 17576                                  40²= 64000

27²= 19683                                  41²= 68921

28²= 21952                                  42²= 74088

29²= 24389                                  43²= 79507

30²= 27000                                  44²= 85184

31²= 29791                                  45²= 91125

32²= 32768                                  49²= 97336

33²= 35937                                  502= 103823

34²= 39304                                  51²= 110592

35²= 42875                                   52²= 117649

                                                      53²= 125000

What is the cube root and how to find the cube root of big numbers?

In mathematics, cube root can be defined as the number that was multiplied thrice and resulted in the cube. Now, let’s go through the formula of cube root which is ∛x = y. The sign that is used to represent cube root is called a radical sign and outside it 3 is written which indicates that we are finding cube root. For square root, 2 is written in place of 3 or simply that radical sign is there. There is one more way to represent cube root that is to write it as the exponent of that number.

From 1 to 50, only 3 numbers have perfect cube roots that are 1, 8 and 27.

How to find the cube root of any number?

We can find cube roots by the method of prime factorization. Here are some steps to solve the cube root.

Step1: First apply prime factorization to find factors of that number.

Step2: Then make a group of 3 same factors like 2,2,2 or 5,5,5 and take one common from them.

Step3: Now multiply all the common taken out terms if every factor is included in the group that means the number is a perfect cube otherwise not.

Perfect Cubes

There is no such integer that when multiplied three times yields the result 121, hence 121 is not a perfect cube in this case. Another way to put it is this: a perfect cube is a number whose cube root is a positive integer. The perfect cubes from the first ten naturals are shown in the following table.

Applications of cube root formula

Given below are a few major applications of cube root formula,

• Solve cubic equations.

• Find the dimensions of a cube if the volume is given.

• Provide a more precise dimension of the apartment.

Conclusion

When we multiply a number three times by itself, the resulting number (product) is referred to as the cube of the original number (cube of the original number). Our term “cube” refers to the fact that it is used to indicate the volume of a cube. In other terms, the cube of a number is a number that has been increased to the third power of the exponent.

It is possible to describe the perfect cube as the product of three numbers that are the same or equal to one another. To provide an example, the number 125 is a perfect cube since it is composed of the numbers 53, 5, 5, and 5.