Cube Root

Whenever you come across the word cube root the two words that come into our mind are cube and roots of a tree. Actually the concept is a bit similar in this sense, root actually refers to the primary source of origin. So we should think about what number you should refer to. That cube will give you a particular number that you are looking for.

Cube root of a number x is a number y only when  y×y×y= x. All the nonzero real numbers have one real cube root and along with it a pair of complex conjugate cube roots, and all non zero complex numbers have three different complex roots that are cube roots.

The cube root of any number in brief can be defined as the factor that we multiply by itself three times to get the particular numbers. Remember that the cube root of a number is exactly opposite of the cubing of a number.

The process of cubing is similar to squaring, only that the number is multiplied three times instead of two times as in squaring. The exponent used for cubes is 3, which is also denoted by the superscript³. Examples are 4³ = 4*4*4 = 64 or 8³ = 8*8*8 = 512 etc.

To find the volume of the cube, we have volume = side3, but if we want to find the side of a cube we have to take the cube root of the volume. Thus, we can say that the cube root is the inverse operation of cubing a number. The cube root symbol is 3√.

Let’s suppose we need to find the value of cube root of 2 is a value that is obtained by multiplying that number three times. It is expressed in the form of ‘3√2’. The meaning of cube root is basically the root of a number that is generated by taking the cube of another number. Hence, if the value of 3√2=x, then x3 =2 and we need to find the value of x.

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We can define the cube root of a number as a special value that, when used in a multiplication exactly three times, gives us that number.For example, 3 × 3 × 3 equals 27, so the cube root of 27 is 3.

The Cube Root Symbol

The special symbol given below signifies the "cube root", it is known to be the "radical" symbol (the symbol can be used for square roots) and with a little three to mean cube root.

3√

You can use it like this, the cube root of 27 is : 3√27=3 (we say "the cube root of 27 equals to 3")

Find the Cube of Fraction

You can find the cube of a fraction the same way as you are finding the cube of a number. You just need to multiply the fraction three times. Just take the example of ⅔. You can get the cube of this fractional number by first multiplying the number in the numerator 3 times that is here you can first multiply the number 2 three times, 2×2×2 and as a result you will get 8 that is the Cube of the number 2 which is in your numerator.

Now move towards the denominator, here in your denominator there is 3, you can get its cube by multiplying it 3 times, that is 3×3×3 hereafter cubing the number 3 you are going to get 27 as a result, which is the Cube of your number 3, registered here as the denominator. So as a result you are going to get 8/27. This 8/27 is the Cube of your number ⅔ which you can get either by doing the multiplication of these numbers separately or you can do the multiplicity of the whole fraction three times, that is ⅔ × ⅔ × ⅔. Giving you the result of 8/27.

You Can Also Cube Negative Numbers

Have a look at this:When we cube +5 we generally get +125:  +5 × +5 × +5 = +125

When we cube −5 we get the number −125:  −5 × −5 × −5 = −125. So the cube root of the number −125 is equal to −5

Cube Roots (For Integer Results 1 through 10)

• Cube root of 1 is 1

• Cube root of 8 is 2

• Cube root of 27 is 3

• Cube root of 64 is 4

• Cube root of 125 is 5

• Cube root of 216 is 6

• Cube root of 343 is 7

• Cube root of 512 is 8

• Cube root of 729 is 9

• Cube root of 1000 is 10

What is the Meaning of Cube Root?

The cube root of a number a is that number which when multiplied by itself three times gives the number ‘a’ itself. 

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Let’s see for example, 

23 =8, or the cube root of the number 8 is 2

33 = 27, or the cube root of the number 27 is 3

43 = 64, or the cube root of 64 is 4

53 = 125, or the cube root of 125 is 5

The symbol of the cube root is a3 or 3√a

Thus, the cube root of 125 is represented as 3√125=5 and that of 27 can be represented as 3√27 equals 3 and so on.

We know that the cube of any number is found by multiplying that number three times. And the cube root of a number can be defined as the inverse operation of cubing a number.

For Example:

If the cube of a number 63 = 216

Then the cube root of ∛216 is equal to 6.

Cube root of any largest number can be easily found in four ways:

• Prime factorization Method 

• Long Division Method

• Using Logarithms

• Bisection Method

A Few Properties of Cube Root

• The cube root of all the odd numbers is an odd number. For example ∛125 = 5, ∛27 = 3.

• Cube root of all even natural numbers is even. For example: ∛8 = 2,∛64 = 4.

• The cube root of a negative integer always results in negative.

Let’s Know Cube Roots of Some Numbers

• The cube root of 16 is 2.1598

• The cube root of 5 is 1.7099

• The cube root of 6 is 1.1871

• The cube root of 10 is 2.1544

• The cube root of 12 is 2.2894

• The cube root of 7 is 1.912

• The cube root of 0 is 0 

• The cube root of 20 is 2.7144

What are Perfect Cubes?

A perfect cube of  an integer is that integer which is actually equal to some other integer raised to the third power. We refer to raising the number to the third power as cubing the number.

The example that we just saw also happens to be an example of a perfect cube. A perfect cube can be defined as a cube of a whole number. 27 is a perfect cube because to get the number 27, we need to cube the number 3. Think back to the cube. It's a perfect cube because all the building blocks are whole pieces. To find a perfect cube, we take any whole number and cube it, meaning we multiply it by itself three times. Knowing the perfect cubes will help us to find cube roots easily. If we started with the 1 and found perfect cubes for our numbers up to 10, we would get this list:1 2 3 4 5 6 7 8 9 10.

 Perfect Cube :1 8 27 64 125 216 343 512 729 1000 .

What is a Cube Root Calculator?

Cube root calculator is a tool that will help you to find the cube root of a particular number. This calculator is free. By using the cube root calculator you can find the cube root of a number free without giving any charge.

How can you use a Cube Root Calculator?

To use the cube root calculator follow the steps given below. It will make your work of calculating cube easy.

• Step 1 : You should write any integer or decimal number that you need to find the cube root of in the enter number box.

• Step 2: Click on 'calculate' and you will get the step wise result of the cube root of the number you are looking for.

• Step 3: Click on the reset button and you can re enter the new number and find the cube root of another number.

Questions to be Solved

Question: What is the Cube Root of 30?

Answer: Well, 3 × 3 × 3 = 27 and 4 × 4 × 4 = 64, so we can guess the answer is between 3 and 4.

• Let's try the following 3.5: 3.5 × 3.5 × 3.5 = 42.875

• Let's try  the following 3.2: 3.2 × 3.2 × 3.2 = 32.768

• Let's try the following 3.1: 3.1 × 3.1 × 3.1 = 29.791

Now we are getting closer, but slowly at this point, we can use a calculator and it says:

3.1072325059538588668776624275224...... but the digits just go on and on, without any kind of pattern. So even the calculator's answer can be known only as an approximation !

Question 2:What is the Cube Root of 1728?

Answer: To find the cube root of number such as that of 1728 follow the below step and you can easily get the cube root.The factors of 1728 are given as,1728 = 12 × 12 × 12∛1728 = ∛(12 × 12 × 12)∛1728 = 12