**Selina Concise Class 8 Math Chapter 3 Squares And Square Roots Exercise 3C Solutions**

**EXERCISE 3C**

**(1) Seeing the value of the digit at unit’s place, state which of the following can be square of a number?**

Ans: We know that the ending digit of the square of a number is 0, 1, 4, 5, 6 or 9. So the given numbers can be squares: 3051, 5684 and 50699 i.e. (i), (iii) and (v).

**(2) Squares of which of the following numbers will have 1(one) at their unit’s place?**

Ans: If a number has 1 or 9 at its unit’s place, then square of this number always has 1(one) at its unit place: 81, 139 i.e. (ii) and (iii).

**(3) Which of the following numbers will not have 1(one) at their unit’s place?**

Ans: If a number has 1 or 9 at its unit’s place, then square of this number always has 1(one) at its unit place: 32^{2}, 57^{2}, 265^{2} i.e. (i), (ii) and (v).

**(4) Squares of which of the following numbers will not have 6 at their unit’s place?**

Ans: If the digit at the unit’s place of a number is 4 or 6, then its square will always have 6 at its unit’s place: 35, 23, 98 i.e. (i), (ii) and (v).

**(5) Which of the following numbers will have 6 at their unit’s place:**

Ans: If the digit at the unit’s place of a number is 4 or 6, then its square will always have 6 at its unit’s place: 26^{2}, 34^{2}, 244^{2} i.e. (i), (iii) and (v).

**(6) If a number ends with 3. Zeroes, how many zeroes will its square have?**

Ans: We know that a number ends with n zeroes, its square ends with (2×n) zeroes.

Therefore, a number ends with 3 zeroes, its square ends with (2×3) = 6 zeroes.

**(7) If the square of a number ends with 10 zeroes, how many zeroes will the number have?**

Ans: We know that a number ends with n zeroes, its square ends with (2×n) zeroes.

Therefore, the square of a number ends with 10 zeroes, then the number will have = (10 ÷ 2) = 5 zeroes.

**(8) Is it possible for the square of a number to end with 5 zeroes? Give reason.**

Ans: No it is not possible for the square of a number to end with 5 zeroes. Which is odd, it will always have an even number of zeroes.

**(9) Give reason to show that none of the numbers 640, 81000 and 3600000 is a perfect square.**

Ans: A number having 2, 3, 7 or 8 at the unit place is never a perfect square.

**(10) State, whether the square of the following numbers is even or odd?**

(i) 23 = Odd

(ii) 54 = Even

(iii) 76 = Even

(iv) 75 = Odd

**(11) Give reason to show that none of the numbers 640, 81000 and 3600000 is perfect square.**

Ans: No number has an even number of zeroes.

**(12) Evaluate:**

(i) 37^{2} – 36^{2}

= (37 + 36) (37 – 36)

= 73 × 1

= 73

(ii) 85^{2} – 84^{2}

= (85 + 84) (85 – 84)

= 169 × 1

= 169

(iii) 101^{2} – 100^{2}

= (101 + 100) (101 – 100)

= 201 × 1

= 201

**(13) Without doing the actual addition, find the sum of:**

(i) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

= Sum of first 12 odd natural numbers = (12)^{2} = 144.

(ii) 1 + 3 + 5 + 7 + 9 + ………….. + 39 + 41

= Sum of first 21 odd natural numbers = (21)^{2} = 441.

(iii) 1 + 3 + 5 + 7 + 9 + ….. + 51 + 53

= Sum of first 27 odd natural numbers = (27)^{2} = 729.

**(14) Write three sets Pythagoras triplets such that each set has numbers less than 30**

Ans: natural numbers 6, 8 and 10; 15, 20 and 25; 10, 24 and 26.

(i) 6^{2} + 8^{2} = 10^{2}

⇒ 36 + 64 = 100

⇒ 100 = 100

(ii) (15)^{2} + (20)^{2} = (25)^{2}

⇒ 225 + 400 = 625

⇒ 625 = 625

(iii) (10)^{2} + (24)^{2} = (26)^{2}

⇒ 100 + 576 = 676

⇒ 676 = 676