# Square Root by Prime Factorization Method

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**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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**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

• 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

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