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Q.

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

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a

49, 65, 81, 169, 625, 900,100, 1000

b

8, 36, 49, 81, 169, 625, 900, 1000

c

1, 36, 49, 81, 169, 625, 900,100. 10000

d

8, 65, 81, 169, 625, 900,100. 10000

answer is C.

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Detailed Solution

Concept: Perfect square is the result of multiplying an integer by itself. These figures are positive. For instance, 9 is an example of a square number because it can be expressed as 33.
The inverse, or opposite, operation, of many mathematical operations. The opposite of addition is subtraction, the opposite of multiplication is division, and so on. Finding the square root is the inverse of squares, which we learnt about in a previous lesson on exponents. Keep in mind that a number is multiplied by itself to form its square. The squares of the following whole integers are perfect squares: 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

100^{2} = 100 \times 100 = 10000

So, from above given numbers,
1, 36, 49, 81, 169, 625, 900 and 100 are perfect squares.
Hence, the correct answer is option 3.

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