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Squares And Square Roots

Question
CBSEENMA8002459
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Observe the following pattern and find the missing digits.

112 = 121
1012 = 10210
10012 = 1002001
1000012 = 1 ............. 2 ..............1
100000012 = ........................

Solution

Observing the above pattern, we have

(i) (100001)2 = 10000200001

(ii) (10000001)2 = 100000020000001

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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