Chapter 3: Squares and Square Roots & Cubes and Cube Roots

Solution:-

Let us assume decimal number be ‘a’.

We know that, a × a = a²

So,

a × a = 51.84

a² = 51.84

a = √51.84

The required number is found out by using long division method.

Then,

a = √51.84

a = 7.2

∴7.2 is the decimal number is multiplied by itself and its product is 51.84.

Solution:-

Let us assume decimal fraction be ‘a’.

We know that, a × a = a²

So,

a × a = 84.64

a² = 84.64

a = √84.64

The required number is found out by using long division method.

Then,

a = √84.64

a = 9.2

∴9.2 is the decimal fraction is multiplied by itself and its product is 84.64.

Solution:-

From the question it is given that,

Length of the side of square field = 150 m

We know that, are of square = side × side

So,

Area of the square field = 150 × 150

= 22,500 m²

∴The farmer have to plough 22,500 m² area.

Solution:-

From the question it is given that,

The total number of unit squares is = 256.

Let us assume the number be ‘a’

We know that, a × a = a²

So,

a × a = 256

a² = 256

a = √256

a = √(16 × 16)

a = √16²

a = 16

∴The number of unit squares are 16.

Solution:-

From the question it is given that,

Length of one side of the a cube = 15 m

We know that, volume of cube = (side)³

= 15³

= 15 × 15 × 15

= 3375 m³

∴The volume of cube is 3375 m³.

Solution:-

From the question it is given that,

Length of rectangular field = 80 m

Breadth of rectangular field = 18 m

Then,

Length of diagonal = √(length² + breadth²)

= √(80² + 18²)

= √(6400 + 324)

= √6724

= 82 m

∴The Length of diagonal is 82 m.

Solution:-

Given, perimeter of the square field = 96 m

We know that, perimeter of square = 4 × side

Then,

96 = 4 × side

Side = 96/4

Side = 24 m

So, the length of the side of square = 24 m

Now,

Area of the square field = (side)²

= 24²

= 576 m²

∴The area of the square field is 576m².

Solution:-

From the question it is given that,

Volume of the cube = 512 cm³

We know that,

Volume of cube = side³

512 = side³

By taking cube root on both the side,

³√512 = side

Side = ³√(8 × 8 × 8)

Side = ³√ (8)³

Side = 8 cm

∴The length of each side of a cube is 8 cm.

Solution:-

Let us assume the three number be a, 2a, 3a

Then,

Given, sum of cube of three numbers is 4500

i.e. a³ + (2a)³ + (3a)³ = 4500

a³ + 8a³ + 27a³ = 4500

36a³ = 4500

a³ = 4500/36

a³ = 125

a = ³√125

a = ³√(5 × 5 × 5)

a = ³√(5³)

a = 5

∴The numbers are, a = 5

2a = 2 × 5 = 10

3a = 3 × 5 = 15

Solution:-

Given, side of square room = 6.5 m

So, area of square room = 6.5²

= 6.5 × 6.5

= 42.25 m²