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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

### 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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