**GSEB Solutions for Class 7 Mathematics – Square and Square Root (English Medium)**

GSEB SolutionsMathsScience

**Exercise**

**Solution 1:**

**Solution 2:**

The square of an odd number is an odd number and the square of an even number is an even number.

- 1985

1985 has 5 at its unit’s place.

Hence, the digit at the unit’s place of the square of 1985 will be 5 (5 × 5 = 25).

∴ The square of 1985 is an odd number. - 253

253 has 3 at its unit’s place.

Hence, the digit at the unit’s place of the square of 253 will be 9 (3 × 3 = 9).

∴ The square of 253 is an odd number. - 444

444 has 4 at its unit’s place.

Hence, the digit at the unit’s place of the square of 444 will be 6 (4 × 4 = 16).

∴ The square of 444 is an even number. - 99

99 has 9 at its unit’s place

Hence, the digit at the unit’s place of the square of 99 will be 1 (9 × 9 = 81).

∴ The square of 99 is an odd number.

**Solution 3:**

If a number has x number of zeros as its last digits, the square of the number has 2x zeros as its last digits.

- 20

The number 20 has one zero as its last digit.

Hence, the square of 20 will have 2 × 1= 2 zeros as its last digits. - 200

The number 200 has two zeros as its last digits.

Hence, the square of 200 will have 2 × 2 = 4 zeros as its last digits. - 30

The number 30 has one zero as its last digit.

Hence, the square of 30 will have 2 × 1 = 2 zeros as its last digits. - 700

The number 700 has two zeros as its last digits.

Hence, the square of 700 will have 2 × 2 = 4 zeros as its last digits.

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**Practice – 1**

**Solution 1:**

- 102 = 10 × 10 = 100
- 112 = 11 × 11 = 121
- 132 = 13 × 13 = 169
- 182 = 18 × 18 = 324
- 322 = 32 × 32 = 1024
- 462 = 46 × 46 = 2116

**Practice – 2**

**Solution 1:**

If the given number is a square of a number, it is called a perfect square number.

If your roll number is a perfect square number, it must have either 0, 1, 4, 5, 6 or 9 at its unit place.

If your roll number has 2, 3, 7, or 8 at its unit place, it can never be a perfect square number.

**Solution 2:**

Perfect squares between 1 to 100 are as follows:

1 × 1= 1

2 × 2 = 4

3 × 3 = 9

4 × 4 =16

5 × 5 = 25

6 × 6 = 36

7 × 7 = 49

8 × 8 = 64

9 × 9 = 81

10 × 10 = 100

Hence, there are ten perfect squares between 1 and 100. They are 1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.

**Solution 3:**

If the number is a perfect square it must have 0, 1, 4, 5, 6 or 9 at its units place.

If the number has 2, 3, 7 or 8 at its units place, it can never be a perfect square.

**Solution 4:**

If the number has 2, 3, 7, or 8 at its units place, it can never be a perfect square.

Hence, given below are those numbers wherein looking at their units place, it can be concluded that they are not perfect squares.

2

43

307

2008

2302

28

2167

13

102

1237

**Practice – 3**

**Solution 1:**

1. 752 = 75 × 75 = 5625

The consecutive number to 7 is 8 and 8 × 7 = 56.

Write 25 to the right of the product i.e. 56.

Hence, the square of 75 is 5625.

2. 652 = 65 × 65 = 4225

The consecutive number to 6 is 7 and 7 × 6 = 42.

Write 25 to the right of the product i.e. 42.

Hence, the square of 65 is 4225.

3. 852 = 85 × 85 = 7225

The consecutive number to 8 is 9 and 9 × 8 = 72.

Write 25 to the right of the product i.e. 72.

Hence, the square of 85 is 7225.

4. 1052 = 105 × 105 = 11025

The consecutive number to 10 is 11 and 11 × 10 = 110.

Write 25 to the right of the product i.e. 11025.

Hence, the square of 105 is 11025.

**Practice – 4**

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**Solution 2:**

If the number has 2, 3, 7, or 8 at its units place, it can never be a perfect square.

The unit’s digit in 42 is 2.

∴ 42 is not a perfect square.

The unit’s digit in 50 is 0.

∴ 50 can be a perfect square.

Indivisible factors of 50 = 2 × 5 × 5

Here, the prime factor 5 forms a pair but the prime factor 2 does not form a pair.

∴ 50 is not a perfect square.

**Practice – 5**

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