As the name suggests in this method we need to find the prime factors of the perfect square.
Square root of 196 by prime factorization method.
Since the number is a perfect square you will be able to make an exact number of pairs of prime factors.
I decompose the number inside the square root into prime factors.
Notice 196 2 2 7 7 since there is an even number of prime factors and they can be grouped in identical pairs we know that.
The square root of 1764 by prime factorization we get 1764 2 x 2 x 3 x 3 x 7 x 7.
The product obtained in step v is the required square root.
Thew following steps will be useful to find square root of a number by prime factorization.
Ii inside the square root for every two same numbers multiplied one number can be taken out of the square root.
1764 2 x 2 x 3 x 3 x 7 x 7 2 x 3 x 7 therefore 1764 42.
Find the product of factors obtained in step iv.
Square root by prime factorization method example 1 find the square root.
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Square root of 7744 in prime factorization method 6640952 the area of neck and bottom of a bottle are 4cm square and 100cm square respectively.
Prime factorization method for finding square roots examples with a square root without a square root determine the square root of 196.
The perfect square is factorized into its prime factors by successive division.
Take one factor from each pair.
Finding the square root of a number without a calculator.
Iii combine the like square root terms using mathematical operations.