Question

Identify the perfect squares among the following numbers
1, 2, 3, 8, 36, 49, 65, 67, 71, 81, 169, 625, 125, 900, 100, 1000, 10000

Answer 1

Hint: Perfect square – It is the product of some integer with itself. These numbers are non-negative.For example, 9 is a square number, since it can be written as $ 3 \times 3 $

Complete step-by-step answer:
Many mathematical operations have an inverse, or opposite, operation. Subtraction is the opposite of addition, division is the inverse of multiplication, and so on. Squaring, which we learned about in a previous lesson (exponents), has an inverse too, called "finding the square root." Remember, the square of a number is that number times itself. The perfect squares are the squares of the whole numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 …
 $ {1^2} = 1 \times 1 = 1 $
 $ {6^2} = 6 \times 6 = 36 $
 $ {7^2} - 7 \times 7 = 49 $
 $ {9^2} = 9 \times 9 = 81 $
 $ {13^2} = 13 \times 13 = 169 $
 $ {25^2} = 25 \times 25 = 625 $
 $ {30^2} = 30 \times 30 = 900 $
 $ {10^2} = 10 \times 10 = 100 $
So, from above given numbers,
1, 36, 49, 81, 169, 625, 900 and 100 are perfect squares.

Note: In base 10, a square number can end only with digits 0, 1, 4, 5, 6 or 9 as follows :
If the last digit of a number is 0, its square ends in 0 (in fact, the last two digits must be 00)
If the last digits of a number is 1 or 9, its squares ends in 1
If the last digits of a number is 2 or 8, its squares ends in 4
If the last digits of a number is 3 or 7, its squares ends in 9
If the last digits of a number is 4 or 6, its squares ends in 6
If the last digits of a number is 5, its square ends in 5 (in fact, the last two digits must be 25).