## square root

### y=√x

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5, because 5 x 5 = 25. The square root symbol is √.

There are different methods to find the square root of a number. One common method is the prime factorization method, which involves finding the prime factors of the number and grouping them in pairs. For example, to find the square root of 72:

1. Write the prime factorization of 72: 2 x 2 x 2 x 3 x 3

2. Group the prime factors in pairs: (2 x 2) x (2 x 3) x 3

3. Take one factor from each pair and multiply them: 2 x 2 x 3 = 12

4. The result is the square root of the original number: √72 = 12

Another method to find the square root of a number is the long division method. This method involves dividing the number into smaller parts and finding the square root of each part. Then, the square roots are combined to find the square root of the original number. This method is useful for finding square roots of large numbers or numbers that do not have a simple factorization.

In summary, the square root of a number is a value that, when multiplied by itself, gives the original number. There are different methods to find the square root of a number, including the prime factorization method and the long division method.

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