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