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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

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

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
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 3×3 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 … 12=1×1=1 62=6×6=36 72−7×7=49 92=9×9=81 132=13×13=169 252=25×25=625 302=30×30=900 102=10×10=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).

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