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Class 8 RD Sharma Solutions – Chapter 3 Squares and Square Roots – Exercise 3.2 | Set 2
  • Last Updated : 06 Apr, 2021

Chapter 3 Squares and Square Roots – Exercise 3.2 | Set 1

Question 11. Which of the following numbers are squares of even numbers?
121, 225, 256, 324, 1296, 6561, 5476, 4489, 373758

Solution:

Only even numbers be the square of even numbers.

So, 256, 324, 1296, 5476, 373758 are even numbers

But 373758 is not a perfect square as unit digit is 8

Therefore, 256, 324, 1296, 5476 are squares of even numbers.



Question 12. By just examining the units digits, can you tell which of the following cannot be whole squares?

(i) 1026

Solution:

As unit digit is 6

Therefore,it can be a perfect square.

(ii) 1028

Solution:

As unit digit is 8

Therefore, it can not be a perfect square.

(iii)1024

Solution:

As unit digit is 4

Therefore, it can be a perfect square.

(iv) 1022

Solution:

As unit digit is 2

Therefore, it can not be a perfect square.

(v) 1023

Solution:



As unit digit is 3

Therefore, it can not be a perfect square.

(vi) 1027

Solution:

As unit digit is 7

Therefore, it can not be a perfect square.

Question 13. Which of the numbers for which you cannot decide whether they are squares.

Solution:

We know that the natural numbers ending with digits such as 0, 1, 4, 5, 6 or 9 cannot be decided surely whether they are squares or not.

Question 14. Write five numbers which you cannot decide whether they are square just by looking at the unit’s digit.

Solution:

We know that any natural number ending with 0, 1, 4, 5, 6 or 9 can be or cannot be a square number.

Here are the five examples which you cannot decide whether they are square or not just by looking at the units place:

(i) 2061

The unit digit is 1. So, it may or may not be a square number

(ii) 1069

The unit digit is 9. So, it may or may not be a square number

(iii) 1234

The unit digit is 4. So, it may or may not be a square number

(iv) 56790

The unit digit is 0. So, it may or may not be a square number

(v) 76555

The unit digit is 5. So, it may or may not be a square number

Question 15. Write true (T) or false (F) for the following statements.

(i) The number of digits in a square number is even.

Solution:

False, because 121 is a square number with odd number of digits.

(ii) The square of a prime number is prime.

Solution:

False, because the square of 5(which is prime) is 25(which is not prime).

(iii) The sum of two square numbers is a square number.

Solution:

False, because sum of 12 and 22 is 5 which is not a square number.

(iv) The difference of two square numbers is a square number.

Solution:

False, Difference of 42 = 16 and 32 = 9 is 7 which is not a prefect square.

(v) The product of two square numbers is a square number.

Solution:

True, 32=9, 42=16 Product is 144 which is square of 12.

(vi) No square number is negative.

Solution:

True, because (-3)2 is 9, which is not negative.

(vii) There is no square number between 50 and 60.

Solution:

True, because as there is no square number between them.

(viii) There are fourteen square number up to 200.

Solution:

True, because square numbers up to 200 are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196.

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