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How do you calculate square root "in hand"?


The best method for calculating the square root is to break the number into its prime factors. For example:

64 root. We break down 64 its prime factors:

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

So 64 equals 26.

We divide the exponent 6 by the square root exponent (which is 2), and remove the root number.
6 divided by 2 equals 3 so the answer is 23, that is, 8. Summing up:

So root of 64 is equal to 8. Learn more about prime factor decomposition.