1. Find 4th root of 10000 using prime factorization method

Solution:
First find factors of 10000

2	10000
2	5000
2	2500
2	1250
5	625
5	125
5	25
5	5
	1

`10000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 5`

`10000 = 2^4 * 5^4`

`root (4)(10000) = root (4)(2^4 * 5^4)` (Taking 4th root)

`= 2 × 5`

`= 10`

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2. Find 4th 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 4th root
`:. root (4)(4096)=root (4)(2^12)`

`=2^3`

`=8`

`:.` 4096 is a perfect `4^(th)` power

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3. Find 3rd 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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