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Squares And Square Roots

Question

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The sum of first ‘n’ odd natural numbers is

n² – 1

n²

n² + 1

Solution

B.

n²

Some More Questions From Squares and Square Roots Chapter

How many natural numbers lie between 92 and 10²? Between 11² and 12²?

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

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