# Square Root by Prime Factorization Method

Square root by prime factorization method

Procedure

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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Practice

Q.1 Find the square root by prime-factorization method.

1) 4096 2) 8281 3) 529

Q.2 A welfare association collected \$202500 as a donation from the residents. If each paid as many dollars as there were residents, find the number of residents.

Q.3 The length and width of a rectangular hall is 24m and 18m. What is the largest straight line that can be drawn in the floor of the hall.

Squares and Square roots

Introduction of Squares and Square Roots
Perfect Squares or not
Properties of Square Numbers
Short cut method to find squares
Introduction of Square Roots
Properties of Square Roots
Square root by Prime factorization method
Square root by long division method
Square root of rational numbers
Square root of Decimals
Square root by estimation method

From squares and square roots to Exponents