Contents

**Squares and Square Roots – Maharashtra Board Class 6 Solutions for Mathematics (English Medium)**

MathematicsGeneral ScienceMaharashtra Board Solutions

### Exercise-24

**Solution 1:**

- 5

Square of 5

= 5 × 5

= 25 - 10

Square of 10

= 10 × 10

= 100 - 16

Square of 16

= 16 × 16

= 256 - 25

Square of 25

= 25 × 25

= 625 - 110

Square of 110

= 110 × 110

= 12,100

### Exercise-25

**Solution 1:**

- 6
^{2}

Square of six

= 6 × 6

= 36 - 11
^{2}

Square of eleven

= 11 × 11

= 121 - 14
^{2}

Square of fourteen

= 14 × 14

=196 - 65
^{2}

Square of sixty-five

= 65 × 65

= 4225 - 552

Square of fifty-five

= 55 × 55

= 3025 - 18
^{2}

Square of eighteen

= 18 × 18

= 324 - 67
^{2}

Square of sixty-seven

= 67 × 67

= 4489 - 109
^{2}

Square of one hundred and nine

= 109 × 109

=11,881 - 121
^{2}

Square of one hundred and twenty-one

= 121 × 121

=14,641 - 112
^{2}

Square of one hundred and twelve

= 112 × 112

=12,544 - 91
^{2}

Square of ninety-one

= 91 × 91

= 8,281 - 200
^{2}

Square of two hundred

= 200 × 200

= 40,000

### Exercise-26

**Solution 1:**

- 85

The number formed by the digits in the number, other than 5 in the units place = 8

The number following this number = 9

The product of these two numbers = 8 × 9 = 72

The number obtained by writing 25 in front of this number = 7225

∴ 85^{2}= 7,225 - 55

The number formed by the digits in the number, other than 5 in the units place = 5

The number following this number = 6

The product of these two numbers = 5 × 6 = 30

The number obtained by writing 25 in front of this number = 3025

∴ 55^{2}= 3,025 - 75

The number formed by the digits in the number, other than 5 in the units place = 7

The number following this number = 8

The product of these two numbers = 7 × 8 = 56

The number obtained by writing 25 in front of this number = 5625

∴ 75^{2}= 5,625 - 95

The number formed by the digits in the number, other than 5 in the units place = 9

The number following this number =10

The product of these two numbers = 9 × 10 = 90

The number obtained by writing 25 in front of this number = 9025

∴ 95^{2}= 9,025 - 115

The number formed by the digits in the number,

ther than 5 in the units place = 11

The number following this number = 12

The product of these two numbers = 11 × 12 = 132

The number obtained by writing 25 in front of this number = 13225

∴ 115^{2}= 13,225 - 205

The number formed by the digits in the number, other than 5 in the units place = 20

The number following this number = 21

The product of these two numbers = 20 × 21 = 420

The number obtained by writing 25 in front of this number = 42025

∴ 205^{2}= 42,025 - 185

The number formed by the digits in the number, other than 5 in the units place = 18

The number following this number = 19

The product of these two numbers = 18 ×1 9 = 342

The number obtained by writing 25 in front of this number = 34225

∴ 185^{2}= 34,225 - 105

The number formed by the digits in the number, other than 5 in the units place = 10

The number following this number = 11

The product of these two numbers = 10 × 11 = 110

The number obtained by writing 25 in front of this number = 11025

∴ 105^{2}= 11,025

### Exercise-27

**Solution 1(1):**

**Solution 1(2):**

**Solution 1(3):**

**Solution 1(4):**

**Solution 1(5):**

**Solution 1(6):**

**Solution 1(7):**

**Solution 1(8):**

**Solution 1(9):**

**Solution 1(10):**