1. Find Cube root of 64 using prime factorization method

Solution:
First find factors of 64

2	64
2	32
2	16
2	8
2	4
2	2
	1

`64=2 xx 2 xx 2 xx 2 xx 2 xx 2`

`64=2^6`

Taking cuberoot
`:. root (3)(64)=root (3)(2^6)`

`=2^2`

`=4`

`:.` 64 is a perfect cube

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2. Find Cube root of 125 using prime factorization method

Solution:
First find factors of 125

5	125
5	25
5	5
	1

`125=5 xx 5 xx 5`

`125=5^3`

Taking cuberoot
`:. root (3)(125)=root (3)(5^3)`

`=5`

`:.` 125 is a perfect cube

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3. Find Cube root of 1000 using prime factorization method

Solution:
First find factors of 1000

2	1000
2	500
2	250
5	125
5	25
5	5
	1

`1000 = 2 × 2 × 2 × 5 × 5 × 5`

`1000 = 2^3 * 5^3`

`root (3)(1000) = root (3)(2^3 * 5^3)` (Taking cuberoot)

`= 2 × 5`

`= 10`

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4. Find Cube root of 4096 using prime factorization method

Solution:
First find factors of 4096

2	4096
2	2048
2	1024
2	512
2	256
2	128
2	64
2	32
2	16
2	8
2	4
2	2
	1

`4096=2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2 xx 2`

`4096=2^12`

Taking cuberoot
`:. root (3)(4096)=root (3)(2^12)`

`=2^4`

`=16`

`:.` 4096 is a perfect cube

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