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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