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Squares and Square Roots

  • If a natural number m can be expressed as n2, where n is also a natural number, then m is a square number. The square numbers are also called perfect squares.

Examples: 1, 4, 9, 16, 25, 36 … are perfect squares.

 

  • Prime factorization method of finding the square roots of numbers

 

The square root of 67600 can be found by prime factorization method as follows:

The number 67600 can be prime factorized as:

2 × 2 × 2 × 2 × 5 × 5 × 13 × 13

The numbers, 2, 2, 5, 13, occur in pairs. Therefore,

 

Example: Find the smallest number by which 252 can be multiplied to make it a perfect square.

Solution: We have, 252 = 2 × 2 × 3 × 3 × 7

The number 7 does not occur in pair. Therefore, if we multiply 252 by…

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