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Squares And Square Roots

Question
CBSEENMA8002389
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Find the perfect square numbers between (i) 30 and 40 and (ii) 50 and 60.

Solution

Since, 1 x 1 = 1
         2 x 2 = 4
         3 x 3 = 9
         4 x 4 = 16
         5 x 5 = 25
         6 x 6 = 36
         7 x 7 = 49
Thus, 36 is a perfact square number between 30 and 40.
Since, 7 x 7 = 49 and 8 x 8 = 64. it mean there is no perfect number between 49 and 64, and thus there is not perfect number between 50 and 60.

Some More Questions From Squares and Square Roots Chapter

How many non-square numbers lie between the following pairs of numbers:
(i) 1002 and 1012 (ii) 902 and 912
(iii) 10002 and 10012

Find whether each of the following numbers is a perfect square or not?

(i) 121 (ii) 55 (iii) 81

(iv) 49 (v) 69

Do you think the reverse is also true, i.e. is the sum of any two consecutive positive integers is perfect square of a number? Give example to support your answer.

The difference between the squares of two consecutive natural numbers is equal to the sum of the two numbers.

Write the square, making use of the above pattern.

(i) 1111112 (ii) 11111112

Can you find the square of the following numbers using the above pattern?

(i) 66666672 (ii) 666666672

What will be the unit digit of the squares of the following numbers?

(i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555

The following numbers are obviously not perfect squares. Give reason.

(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050

The squares of which of the following would be odd numbers?

(i) 431 (ii) 2826 (iii) 7779 (iv) 82004

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