NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.1 Part 2

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Properties of square numbers are given in image

Properties of Square Numbers

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Question: 2 The following numbers are obviously not perfect squares. Give reasons.

(i) 1057

(ii) 23453

(iii) 7928

(iv) 222222

(v) 64000

(vi) 89722

(vii) 222000

(viii) 505050

Answer:

Perfect square numbers contain their unit’s place digit 1, 4, 5, 6, 9 and even numbers of 0.

(i) 1057 is not a perfect square because its unit’s place digit is 7.

(ii) 23453 is not a perfect square because its unit’s place digit is 3.

(iii) 7928 is not a perfect square because its unit’s place digit is 8.

(iv) 222222 is not a perfect square because its unit’s place digit is 2.

(v) 64000 is not a perfect square because its unit’s place digit is odd number 0.

(vi) 89722 is not a perfect square because its unit’s place digit is 2.

(vii) 222000 is not a perfect square because its unit’s place digit is odd number 0.

(viii) 505050 is not a perfect square because its unit’s place digit is odd number 0.

Question: 3 The squares of which of the following would be odd number:

(i) 431

(ii) 2826

(iii) 7779

(iv) 82004

Answer:

Here, the squares of the any numbers unit digit are the squares of the unit’s place digit of given number.

(i) 431 – Unit’s digit of given number is 1 and square of 1 is 1. Therefore, square of 431 would be an odd number.

(ii) 2826 – Unit’s digit of given number is 6 and square of 6 is 36. Therefore,

square of 2826 would not be an odd number.

(iii) 7779 – Unit’s digit of given number is 9 and square of 9 is 81. Therefore, square of 7779 would be an odd number.

(iv) 82004 – Unit’s digit of given number is 4 and square of 4 is 16. Therefore, square of 82004 would not be an odd number.

Question: 4 Observe the following pattern and find the missing digits:

Answer:

In given pattern, squares of the given numbers have the same number of zeroes before and after the digit 2 as it was in the original number.

= 121