Question

2. The following numbers are obviously not perfect squares. Give reason.
6) 1057
(ii) 23453
(ii) 7928
(v) 222222
(v) 64000
(vi) 89722
(vii) 222000 (vi) 505050​

Answer 1

Step-by-step explanation:

Ncert solutions

Grade 8

Mathematics

Science

Chapters in NCERT Solutions - Mathematics , Class 8

Exercises in Squares and Square Roots

Question 2

Q2) 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

Solution

Transcript

Solution:

(i) Since, perfect square numbers contain their unit’s place digit 1, 4, 5, 6, 9 and even numbers of 0. Therefore 1057 is not a perfect square because its unit’s place digit is 7.

(ii) Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9 and even number of 0. Therefore 23453 is not a perfect square because its unit’s place digit is 3.

(iii) Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9 and even number of 0. Therefore 7928 is not a perfect square because its unit’s place digit is 8.

(iv) Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9 and even number of 0. Therefore 222222 is not a perfect square because its unit’s place digit is 2.

(v) Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9 and even number of 0. Therefore 64000 is not a perfect square because its unit’s place digit is single 0.

(vi) Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9 and even number of 0. Therefore 89722 is not a perfect square because its unit’s place digit is 2.

(vii) Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9 and even number of 0. Therefore 222000 is not a perfect square because its unit’s place digit is triple 0.

(viii) Since, perfect square numbers contain their unit’s place digit 0, 1, 4, 5, 6, 9 and even number of 0. Therefore 505050 is not a perfect square because its unit’s place digit is 0.

Answer 2

Answer:

We know that natural numbers ending in the digits 0,2,3,7 and 8 are not perfect squares.

(i) 1057 ⟶ ends with 7

(ii) 23453 ⟶ ends with

(iii) 7928 ⟶ ends with 8

(iv) 222222 ⟶ ends with 2

(v) 64000 ⟶ ends with 0 \:

(vi) 89722 ⟶ ends with 2

(vii) 222000 ⟶ ends with 0

(viii) 505050 ⟶ ends with 0

So,the following numbers are obviously not perfect square.