Exercise 5.1 maths square and square root

 Q-1. What will the unit digit of the square of the following numbers?

1. 11

Solve: 1 × 1 = 1

Ans: 1


2. 272

Solve: 2 × 2 = 4

Ans: 4

3. 799

Solve: 9 × 9 = 81

Ans: 1

4. 3853

Solve: 3 × 3 = 9

Ans: 9

5. 1234

Solve: 4 × 4 = 16

Ans: 6

6. 7437

Solve: 7 × 7 = 49

Ans: 9

7. 52692

Solve: 2 × 2 = 4

Ans: 4

8. 99920

Solve: 0 × 0 = 0

Ans: 0

9. 12796

Solve: 6 × 6 = 36

Unit Digit Ans: 6

10. 55555

Solve: 5 × 5 = 25

Unit Digit Ans: 5

Q-2. The following numbers are obviously not perfect squares. Give reason.

a) 1057

Ans: No, because it ends with 7.

b) 23453

Ans: No, because it ends with 3.

c) 7928

Ans: No, because it ends with 8.

d) 222222

Ans: No, because it ends with 2.

e) 6000

Ans: No, because it ends with 0.

f) 89722

Ans: No, because it ends with 2.

g) 222609

Ans: No, because it ends with 9.

h) 505050

Ans: No, because it ends with 0.

Q-3. The square of each of the following would be odd numbers:

a) 431

Ans: odd number

b) 2836

Ans: even number

c) 7779

Ans: odd number

d) 8204

Ans: even number

Q-4. Observe the following pattern and find the missing digits:

11² = 121

101² = 10201

1001² = 1002001

10000² = 10000200001

100000² = 1000002000001

Q-5. Observe the following pattern and supply the missing numbers:

11² = 121

101² = 10201

1001² = 1002001

10001² = 100020001

10101 × 10101 = 10203040504030201

Q-6. Using the given pattern, find the missing numbers:

1. 1² + 2² + 2² = 3²

2. 2² + 3² + 6² = 7²

3. 3² + 4² + 12² = 13²

4. 4² + 5² + 20² = 21²

5. 5² + 6² + 30² = 31²

6. 6² + 7² + 42² = 43²

Q-7. Without adding, find the sum:

1. 1 + 3 + 5 + 7 + 9

Solve: 5 digits here = 5² = 25

Ans: 25

2. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

Solve: 10 digits here = 10² = 100

Ans: 100

3. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Solve: 12 digits here = 12² = 144

Ans: 144

Q-8.

i) Express 49 as the sum of 7 odd numbers:

Solve: 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49

Ans: 49

ii) Express 121 as the sum of 11 odd numbers:

Solve: 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 = 121

Ans: 121

Q-9How many numbers lie between square of the following:

1. 12 and 13

Solve: Between 12² and 13²

Ans: 2 × 12 = 24 numbers

2. 25 and 26

Solve: Between 25² and 26²

Ans: 2 × 25 = 50 numbers

3. 99 and 100

Solve: Between 99² and 100²

Ans: 2 × 99 = 198 numbers


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