Cubic and cube roots

Cubic and cube roots

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.

Lessons

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
• 1.
Understanding the negative cube roots of the following
a)
${^3}\sqrt{27}$
- ${^3}\sqrt{27}$
${^3}\sqrt{-27}$

• 2.
Find the cube roots
a)
${^3}\sqrt{-4913}$

b)
${^3}\sqrt{1331}$

c)
$-{^3}\sqrt{2197}$