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6. N
th
root of a number using prime factorization method
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`