# NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.1

NCERT Solutions for Class 8 Maths Chapter 7 Exercise 7.1 (Ex. 7.1) Cube and Cube Roots updated for academic session 2021-2022 free to download or use online. All the contents of class 8 Maths chapter 7 is updated for CBSE and State Boards (Like UP Board, MP Board, Haryana, Rajasthan, Gujrat, and other also).

Here we will learn about Cubes, Properties of cubes of numbers, Cube roots, and how to find the cube roots by factorisation method.

## Class 8 Maths Chapter 7 Exercise 7.1 Solution

 Class: 8 Mathematics Chapter: 7 Cube and Cube Roots Exercise: 7.1 Solutions in Hindi and English

### Class 8 Maths Chapter 7 Exercise 7.1 Solution in Videos

Class 8 Maths Chapter 7 Exercise 7.1 Solution
Class 8 Maths Chapter 7 Exercise 7.1 Explanation

#### Cubes of a Number

We know that when a number is multiplied by itself, we get the square of that number. If the number ‘x’ is multiplied by itself, then square of x = x ´ x = x²
Similarly, if a number is multiplied by itself 3 times, we get cube of that number. If x is a number.
then, cube of x = x X x X x = x³
2³ = 2 x 2 x 2 = 8 Thus, cube of 2 is 8.
3³ = 3 x 3 x 3 = 27 Thus, cube of 3 is 27.

#### Perfect Cube

A natural number is said to be a perfect cube, if it is the cube of a natural number.
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64.
Thus, 1, 8, 27, 64, are perfect cubes.

###### Here are the cubes of first 10 natural numbers:
Number a x a x a = a³ Result
1 1 x 1 x 1 = 1³ 1
2 2 x 2 x 2 = 2³ 8
3 3 x 3 x 3 = 3³ 27
4 4 x 4 x 4 = 4³ 64
5 5 x 5 x 5 = 5³ 125
6 6 x 6 x 6 = 6³ 216
7 7 x 7 x 7 = 7³ 343
8 8 x 8 x 8 = 8³ 512
9 9 x 9 x 9 = 9³ 729
10 10 x 10 x 10 = 10³ 1000

##### Properties of Cubes of Numbers

From the above table, it is observed that:

• 1. 1, 8, 27, 64, 125, …….are the cubes of natural numbers.
• 2. The cubes of even numbers are even and the cubes of odd numbers are odd.
• 3. In a perfect cube, each prime number appears three times in its prime factorisation.
• 4. Cube of a negative number is negative. For example: (-2)³ = (-2) x (-2) x (-2) = -8, (-3)³ = (-3) x (-3) x (-3) = -27
• 5. Cubes of the numbers ending with 0, 1, 4, 5, 6 and 9, also end with the same digits.
• 6. Cubes of the numbers ending with 2 will end with 8 and cube of the numbers ending with 8 will end with 2.
• 7. Cubes of numbers ending with 3 and 7 will end with 7 and 3 respectively.
##### To Find Whether the Given Number is a Perfect Cube

Step 1: Write the given number as a product of its prime factors.
Step 2: Group the factors such that three identical prime factors make one group.
Step 3: If no factor is left over, then the given number is a perfect cube otherwise not.
Step 4: To find the natural number whose cube is the given number, take one number from each group and multiply them. The product of the numbers so obtained will be the required number.

##### Find the cube of the following number: (i) 11 (ii) 12 (iii) 30 (iv) 41

(i) Cube of 11 = (11)³ = 11 x 11 x 11 = 1331
(ii) Cube of 12 = (12)³ = 12 x 12 x 12 = 1728
(iii) Cube of 30 = (30)³ = 30 x 30 x 30 = 27000
(iv) Cube of 41 = (41)³ = 41 x 41 x 41 = 68921

##### What is the definition of cube root?

The cube root of a number is the factor that we multiply by itself three times to get that number.

##### What are cube roots used for?

The cube root is often used to solve cubic equations. In particular, it can be used to solve for the dimensions of a three-dimensional object of a certain volume.

##### The volume of a cubical box is 0.027 m. Find the length of the edge of the box.

Length of each edge = ∛ (volume of cube)
= ∛0.027 =
∛27 /∛1000 = 3/10
Hence, the length of the edge of the cubical box is 3/10 m or 0.3 m.      