Question

Make a list of all perfect squares from 1 to 500.

Answer 1

The perfect square numbers from 1 to 500 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441 and 484 : 22 in all. There are 21 perfect square numbers between 1 to 500.

Answer 2

The list of all perfect squares from 1 to 500 are as follows:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484.

Concept used :

Perfect square:

If all the prime factors of a natural number can be paired then it is a perfect square.

Explanation:

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

11² = 121

12² = 144

13² = 169

14² = 196

15² = 225

16² = 256

17² = 289

18² = 324

19² = 361

20² = 400

21² = 441

22² = 484

For examples :

Check whether the given number is a perfect square or not.

(1) We first find the prime factors of 252 By prime factorization.

Hence,

252 = 2 x 2 x 3 x 3 x 7

252 = (2 × 2) × (3 × 3) × 7

Here, we see that 2 and 3 occur in pairs but 7 needs a pair.

Hence, 252 is not a perfect square.

(2) 144 = (2 × 2) × (2 × 2 ) × ( 3 × 3)

Here, each factor is in pairs

Hence, 144 is a perfect square.

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