## Chapter 6 Squares and Square Roots Exercise 6.3

**Question 1: What could be the possible ‘one’s’ digits of the square root of each of the following numbers?**

i. 9801

ii. 99856

iii. 998001

iv. 657666025

Answer:

i. 9801

ii. 99856

iii. 998001

iv. 657666025

Answer:

i. The unit’s digit of 9801 is 1. If the number has the unit digit as 1, then its square root will end with 1, 9.

ii. The unit’s digit of 99856 is 6. If the number has the unit digit as 6, then its square root will end with 4, 6.

iii. The unit’s digit of 998001 is 1. If the number has the unit digit as 1, then its square root will end with 1, 9.

iv. The unit’s digit of 657666025 is 5. If the number has the unit digit as 5, then its square root will end with 5.

**Question 2: Without doing any calculation, find the numbers which are surely not perfect squares.**

i. 153

ii. 257

iii. 408

iv. 441

Answer:

i. No, 153 is not a perfect square because its unit digit is 3.

i. 153

ii. 257

iii. 408

iv. 441

Answer:

ii. No, 257 is not a perfect square because its unit digit is 7.

iii. No, 408 is not a perfect square because its unit digit is 8.

iv. Yes, 441 is a perfect square because its unit digit is 1.

**Question 3: Find the square roots of 100 and 169 by the method of repeated subtraction.**

Answer:

Answer:

**Question 4: Find the square roots of the following numbers by the Prime Factorisation Method.**

**i. 729**

ii. 400

iii. 1764

iv. 4096

v. 7744

vi. 9604

vii. 5929

viii. 9216

ix. 529

x. 8100

Answer:

ii. 400

iii. 1764

iv. 4096

v. 7744

vi. 9604

vii. 5929

viii. 9216

ix. 529

x. 8100

Answer:

i.

ii.

iii.

iv.

v.

vi.

vii.

viii.

ix.

x.

**Question 5: For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.**

i. 252

ii. 180

iii. 1008

iv. 2028

v. 1458

vi. 768

Answer:

i. 252

ii. 180

iii. 1008

iv. 2028

v. 1458

vi. 768

Answer:

i.

ii.

iii.

iv.

v.

vi.

**Question 6: For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.**

i. 252

ii. 2925

iii. 396

iv. 2645

v. 2800

vi. 1620

Answer:

i. 252

ii. 2925

iii. 396

iv. 2645

v. 2800

vi. 1620

Answer:

i.

ii.

iii.

iv.

v.

vi.

**Question 7: The students of Class VIII of a school donated Rs 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.**

Answer:

Answer:

Total amount donated = ₹2401

Let the number of students = x

Amount of donation by each student = ₹x

Total students = 49

Amount donated by each student = ₹49

Therefore, the number of students are 49 and the money donated each one of them is ₹49.

**Question 8: 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.**

Answer:

Answer:

Total plants to be planted = 2025

Let the number of rows = x

Let the number of plants in a row = x

Total rows = 45

Total plants in a row = 45

Therefore, the number of rows is 45 and number of plants to be planted in each row is 45.

**Question 9: Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.**

Answer:

Answer:

**Question 10: Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.**

**Answer:**

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