Perfect Square – Tips and Tricks

Some Tricks and Tips for Perfect Squares are given below.

Square of a Number Ending in 5: To find square of a number ending in 5, multiply the digit before 5 with next digit and append 25. For example, 75²= 7×8(25) = 5625

Square of Numbers Close to 100: For numbers close to 100, express the square as (100 – x)²= 100² – 200x + x². This simplifies calculations, especially for mentally calculating squares.

Odd Number Squares: Square of any odd number is an odd number. If n is an odd number, then n² is odd.

Even Number Squares: Square of any even number is an even number. If m is an even number, then m² is even.

Difference of Squares: Use difference of squares formula, a²− b²= (a+b)(a−b). This can help in factoring or simplifying expressions.

Square of a Sum: (a+b)² = a² + 2ab + b²

Square of a Difference: (a−b)² = a² − 2ab + b²

Observations on Perfect Squares

Perfect numbers end with any one of these digits 0, 1, 4, 5, 6, or 9. Also some observations on perfect squares are,

• Numbers ending with 3 and 7 have 9 as units place digit in their square number.
• Numbers ending with 5 have 5as units place digit in their square number.
• Numbers ending with 4 and 6 will have 6 as units place digit in their square number.
• Numbers ending with 2 and 8 will have 4 as units place digit in their square number.
• Numbers ending with 1 and 9 will have 1 as units place digit in their square number.

How many Perfect Squares are between 1 and 100?

There are 8 perfect squares between 1 and 100 (excluding 1 and 100). They are,

4, 9, 16, 25, 36, 49, 64 and 81

How many Perfect Squares are between 1 and 1000?

There are 30 perfect squares between 1 and 1000. They are,

4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900 and 961

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Perfect Square is a number obtained by multiplying a whole number by itself, like 4 which is obtained when 2 is multiplied by itself, i.e. 2 × 2 = 4, thus 4 is a perfect square. In mathematical terms, the perfect square is expressed as a².

In this article, we have covered the meaning and definition of perfect squares, methods of finding perfect squares, and a list of perfect squares and applications.