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.

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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

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