# Cubic and cube roots

##### Examples

###### Lessons

##### Practice

###### Free to Join!

StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.

#### Easily See Your Progress

We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.#### Make Use of Our Learning Aids

#### Earn Achievements as You Learn

Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.#### Create and Customize Your Avatar

Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.

###### Topic Notes

Whenever we see "roots", let it be cubic roots or square roots, we know for sure that we will need to do prime factorization to find out the prime factors of the numbers. In this section, we use factors and multiples to find perfect cube whole numbers and cubic roots.

To cube: Raise the number to the third power

Ex: ${3^3}$ $= 3\times 3\times 3 = 27$

${6^3}$ = $6\times 6\times 6 = 216$

To cube root: Finding the three identical factors

Ex: ${^3}\sqrt{64}$ = ${^3}\sqrt{4\times 4\times 4}$ = 4

${^3}\sqrt{125}$ = ${^3}\sqrt{5\times 5\times 5}$ = 5

Perfect Cubes: ${0^3}$= 0

${1^3}$ = 1

${2^3}$ = 8

${3^3}$ = 27

${4^3}$ = 64

${5^3}$ = 125

${6^3}$ = 216

${7^3}$ = 343

${8^3}$ = 512

${9^3}$ = 729

${10^3}$ = 1000

Ex: ${3^3}$ $= 3\times 3\times 3 = 27$

${6^3}$ = $6\times 6\times 6 = 216$

To cube root: Finding the three identical factors

Ex: ${^3}\sqrt{64}$ = ${^3}\sqrt{4\times 4\times 4}$ = 4

${^3}\sqrt{125}$ = ${^3}\sqrt{5\times 5\times 5}$ = 5

Perfect Cubes: ${0^3}$= 0

${1^3}$ = 1

${2^3}$ = 8

${3^3}$ = 27

${4^3}$ = 64

${5^3}$ = 125

${6^3}$ = 216

${7^3}$ = 343

${8^3}$ = 512

${9^3}$ = 729

${10^3}$ = 1000

###### Basic Concepts

2

videos

remaining today

remaining today

5

practice questions

remaining today

remaining today