### 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)2061The unit digit is 1. So, it may or may not be a square number

(ii)1069The unit digit is 9. So, it may or may not be a square number

(iii)1234The unit digit is 4. So, it may or may not be a square number

(iv)56790The unit digit is 0. So, it may or may not be a square number

(v)76555The 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 1

^{2}and 2^{2}is 5 which is not a square number.

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

**Solution:**

False, Difference of 4

^{2 }= 16 and 3^{2 }= 9 is 7 which is not a prefect square.

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

**Solution:**

True, 3

^{2}=9, 4^{2}=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.