square numbers maths

         SQUARES AND SQUARE ROOTS 

Square number - The square of a number is the product of the number with the number itself. 

A given number is a perfect square if its prime factors can be expressed in pairs of equal factors. 

A perfect square number is never negative.

For example - 8^2 = (8×8) = 64

Facts About Squares - 

1. A number ending in 2, 3, 7 or 8 is never a perfect square. 

2. A number ending in an odd number of zeros is never a perfect square. 

3. The square of an even number is always even. 

4. The square of an odd number is always odd. 

5. The ending digits of a square number is 0, 1, 4, 5, 6, or 9 only. 

Note:- It is not necessary that all numbers ending with digits 0, 1, 4, 5, 6, or 9 are square numbers. 

Important Facts- 

1. Numbers ending in an even number of zeros are not necessarily perfect squares. Eg- 3700, 290000, 47000000.

 Practice Questions :- 

1. Find the square of 54 ? 

2. What least number must be added to 5607 to make it a perfect square?

3. Solve √5625 = ?

4. Find the greatest number of four digits which is a perfect square. 

5. Evaluate:  (38)² - (37)²