square root prime factorization
Answers
Step I: Obtain the given number.
Step II: Resolve the given number into prime factors by successive division.
Step III: Make pairs of prime factors such that both the factors in each pair are equal. Since the number is a perfect square, you will be able to make an exact number of pairs of prime factors.
Step IV: Take one factor from each pair.
Step V: Find the product of factors obtained in step IV.
Step VI: The product obtained in step V is the required square root.
Square root by prime factorization method
Example 1
Find the square root of 1156.
1156 = 2 x 578
= 2 x 2 x 289
= 2 x 2 x 17 x 17
∴ √1156 = √( 2 x 2 x 17 x 17 )
√1156 = 2 x 17
√1156 = = 34
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Example 2
Find the square root of 324.
324 = 2 x 162
= 2 x 2 x 81
= 2 x 2 x 3 x 27
= 2 x 2 x 3 x 3 x 9
= 2 x 2 x 3 x 3 x 3 x 3
∴ √324 = √( 2 x 2 x 3 x 3 x 3 x 3 )
√324 = 2 x 3 x 3
√324 = 18
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