HOW TO FIND THE CUBE ROOT OF A NUMBER USING PRIME FACTORIZATION

Example 1 :

Find the cube root of 8.

Solution :

³√8 = ³√(2 x 2 x 2)

= 2

Example 2 :

Find the cube root of 27.

Solution :

³√27 = ³√(3 x 3 x 3)

= 3

Example 3 :

Find the cube root of 512.

Solution :

³√512 = ³√(2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2)

= ³√[(2 x 2 x 2)(2 x 2 x 2)(2 x 2 x 2)]

= 2 x 2 x 2

= 8

Example 4 :

Find the cube root of (27 x 64).

Solution :

³√(27 x 64) = ³√[(3 x 3 x 3)(2 x 2 x 2 x 2 x 2 x 2)]

= ³√[(3 x 3 x 3)(2 x 2 x 2)(2 x 2 x 2)]

= ³√[(3 x 3 x 3)(2 x 2 x 2)(2 x 2 x 2)]

= 3 x 2 x 2

= 12

Example 5 :

Find the cube root of 1000.

Solution :

³√1000 = ³√(2 x 2 x 2 x 5 x 5 x 5)

=³√[(2 x 2 x 2)(5 x 5 x 5)]

= 2 x 5

= 10

Example 6 :

Find the cube root of (8/125).

Solution :

³√(8/125) = ³√8/³√125

=³√(2 x 2 x 2)/³√(5 x 5 x 5)

= 2/5

Example 7 :

Find the cube root of 0.008.

Solution :

³√0.008 = ³√(8/1000)

=³√8/³√1000

= 2/10

= 0.2

Example 8 :

Find the cube root of 0.027.

Solution :

³√0.027 = ³√(27/1000)

=³√27/³√1000

= 3/10

= 0.3

Example 9 :

Find the cube root of 0.343.

Solution :

³√0.343 = ³√(343/1000)

=³√343/³√1000

= 7/10

= 0.7

Example 10 :

Find the cube root of -125.

Solution :

³√-125 = ³√(-5 x -5 x -5)

= -5

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