(a) Between 9² and 10²

Here, n = 9 and n + 1 = 10

 ∴ Natural number between 9² and 10² are (2 × n) or 2 x 9, i.e. 18.

(b) Between 11² and 12²

Here, n = 11 and n + 1 = 12

 ∴ Natural numbers between 11² and 12² are (2 × n) or 2 × 11, i.e. 22.

(i) 727

Since 727 is an odd number.

 ∴ It square is also an odd number.

(ii) 158

Since 158 is an even number.

 ∴ Its square is also an even number.

(iii) 269

Since 269 is an odd number.

 ∴ Its square is also an odd number.

(iv) 1980

Since 1980 is an even number.

 ∴ Its square is also an even number.

(i) In 60, number of zero is 1

 ∴ Its square will have 2 zeros.

(ii) ∵ There are 2 zeros in 400.

 ∴ Its square will have 4 zeros.

Property 6. The difference between the squares of two consecutive natural numbers is equal to the sum of the two numbers.

Property 7. There are 2n non-perfect square numbers between the squares of the numbers n and n + 1.

(i) Between 100² and 101²
Here, n=100 ∴  n x2 = 100 x 2 = 200

∴ 200 non-square numbers lie between 100² and 101² .

(ii)  Between 90² and 91²

Here, n=90  ∴  2 x n = 2 x 90 or 180

∴  180 non-square numbers lie between 90 and 91.

(iii)  Between 1000² and 1001²

Here, n = 1000         ∴  2 x n = 2 x 1000 or 2000
∴  2000 non-square lie between 1000² and 10012.

(i) ∵ Ending digit = 4 and 4² = 16

∴ (1234) will have 6 as the one’s digit.

(ii) ∵ Ending digit is 7 and 7² = 49

∴ (26387)² will have 9 as the one’s digit.

(iii) ∵ Ending digit is 8, and 8² = 64

∴ (52692)² will end in 4.

(iv) ∵ Ending digit is 0.

∴ (99880)² will end in 0.

(v) ∵ 2² = 4

 ∴ Ending digit of (21222)² is 4.

(vi) ∵ 6² = 36

 ∴ Ending digit of (9106)² is 6.