If you want to improve your class 8 Math, Cubes and Cube Roots concepts, then it is super important for you to learn and understand all the formulas.

By using these formulas you will learn about how to calculate Cubes and Cube Roots.

With the help of these formulas, you can revise the entire chapter easily.

## Cubes and Cube Roots Class 8 Maths Formulas

### Cubes

- The cube of a number is that number raised to the power 3 . If $x$ is a number, then $x^{3}=x \times x \times x$.
- A natural number $n$ is a perfect cube if $n=m^{3}$ for some natural number $m$.
- The cube of an odd natural number is odd.
- The cube of an even natural number is even.
- The sum of the cubes of first $n$ natural numbers is equal to the square of their sum. i.e., $1^{3}+2^{3}+3^{3}+\ldots \ldots . .+n^{3}=(1+2+3+\ldots \ldots \ldots+n)^{2}$
- 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. Here, cubes of numbers ending with digits $0,1,4,5,6$ and 9 end with same digits.
- Cube of the number ending with digit 3 ends in 7 and cube of the number ending with digit 7 ends in $3 .$
- Cubes of the number ending with digit 2 ends in 8 or cube of the number ending with digit 8 ends in $2 .$

### Cube root

- The cube root of a number $x$ is the number whose cube is $x$. It is denoted by $\sqrt[3]{x}$.
- For finding the cube root of a perfect cube, resolve it into prime factors; make triplets of similar factors and take the product of prime factors, choosing one out of every triplet.
- For any positive integer $\mathrm{x}$, we have $\sqrt[3]{-x}=-\sqrt[3]{x}$
- For any integers a and b, we have:

(i) $\sqrt[3]{a b}=\sqrt[3]{a} \times \sqrt[3]{b}$

(ii) $\sqrt[3]{\frac{a}{b}}=\frac{\sqrt[3]{a}}{\sqrt[3]{b}}$

Also Read,

Download NCERT Class 8 Maths Book

Download NCERT Class 8 Science Book

Download NCERT Class 8 Science Exemplar

Download NCERT Class 8 Maths Exemplar

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