1. Find Square 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 squareroot
`:. sqrt(64)=sqrt(2^6)`

`=2^3`

`=8`

`:.` 64 is a perfect square

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2. Find Square root of 100 using prime factorization method

Solution:
First find factors of 100

2	100
2	50
5	25
5	5
	1

`100=2 xx 2 xx 5 xx 5`

`100=2^2 * 5^2`

Taking squareroot
`:. sqrt(100)=sqrt(2^2 * 5^2)`

`=2 × 5`

`=10`

`:.` 100 is a perfect square

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3. Find Square root of 900 using prime factorization method

Solution:
First find factors of 900

2	900
2	450
3	225
3	75
5	25
5	5
	1

`900 = 2 × 2 × 3 × 3 × 5 × 5`

`900 = 2^2 * 3^2 * 5^2`

`sqrt(900) = sqrt(2^2 * 3^2 * 5^2)` (Taking square root)

`= 2 × 3 × 5`

`= 30`

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4. Find Square 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 squareroot
`:. sqrt(4096)=sqrt(2^12)`

`=2^6`

`=64`

`:.` 4096 is a perfect square

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