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

1. Can we say whether the following numbers are perfect squares? How do we know?

(i) 1057 (ii) 23453 (iii) 7928

(iv) 222222 (v) 1069 (vi) 2061

Write five numbers which you can decide by looking at their one’s digit that they are not square numbers.

Write five numbers which you cannot decide just by looking at their unit’s digit (or one’s place) whether they are square numbers or not.

Which of 123², 77² 82², 161², 109² would end with digit 1?

Which of the following numbers would have digit 6 at unit place.

(i) 19² (ii) 24² (iii) 26²

(iv) 36² (v) 34²

What will be the “one’s digit” in the square of the following numbers?

(i) 1234 (ii) 26387 (iii) 52698

(iv) 99880 (v) 21222 (vi) 9106

The square of which of the following numbers would be an odd number/an even number?

Why?

(i) 727 (ii) 158 (iii) 269 (iv) 1980

What will be the number of zeros in the square of the following numbers?

(i) 60 (ii) 400

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