MSBSHSE Solutions For Class 8 Maths Part 1 Chapter 3- Indices and Cube Root

MSBSHSE Solutions For Class 8 Maths Part 1 Chapter 3 Indices and Cube Root is one of the best reference material students can rely on. The MSBSHSE Solution for Class 8 module contains all the important topics that can help students score well in the examinations. Facilitators have provided the solutions accurately, depending upon the students grasping abilities to understand the concepts clearly. Every question is explained stepwise for a better understanding of the students.

The best reference guide for the students is the Maharashtra State Board Class 8 Textbooks Part 1 Maths Solutions. Students can analyse their weaker section and can improve on it by thoroughly going through the solutions, after completing every chapter. The PDF of Maharashtra Board Solutions for Class 8 Maths Chapter 3 Indices and Cube Root is provided here. Students can refer and download from the given links. This chapter is based on indices and cube root. Some of the essential topics of this chapter includes the meaning of numbers with rational indices, Cube and Cube root.

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Practice set 3.1 PAGE NO: 15

1. Express the following numbers in index form.
(1) Fifth root of 13
(2) Sixth root of 9
(3) Square root of 256
(4) Cube root of 17
(5) Eighth root of 100
(6) Seventh root of 30

Solution:

In general, n^th root of ‘a’ is expressed as a^1/n. where, a is the base and 1/5 is the index.

So now,

(1) Fifth root of 13

Index form of fifth root of 13is expressed as 13^1/5.

(2) Sixth root of 9

Index form of sixth root of 9 is expressed as 9^1/6.

(3) Square root of 256

Index form of square root of 256 is expressed as 256^1/2.

(4) Cube root of 17

Index form of cube root of 17 is expressed as 17^1/3.

(5) Eighth root of 100

Index form of eighth root of 100 is expressed as 100^1/8.

(6) Seventh root of 30

Index form of seventh root of 30 is expressed as 30^1/7.

2. Write in the form ‘n^th root of a’ in each of the following numbers.

Solution:

In general, a^1/n is written as ‘n^th root of a’.

So now,

(1) (81)^1/4

(81)^1/4 is written as ‘4^th root of 81’.

(2) (49)^1/2

(49)^1/2 is written as ‘square root of 49’.

(3) (15)^1/5

(15)^1/5 is written as ‘5^th root of 15’.

(4) (512)^1/9

(512)^1/9 is written as ‘9^th root of 512’.

(5) (100)^1/19

(100)^1/19 is written as ‘19^th root of 100’.

(6) (6)^1/7

(6)^1/7 is written as ‘7^th root of 6’.

Practice set 3.2 PAGE NO: 16

1. Complete the following table.

Solution:

Generally we can express the number a^m/n as

a^m/n = (a^m)^1/n means ‘n^th root of m^th power of a’.

a^m/n = (a^1/n)^m means ‘m^th power of n^th root of a’.

So by using the above rules let us fill the table:

2. Write the following number in the form of rational indices.
(1) Square root of 5^th power of 121.
(2) Cube of 4^th root of 324.
(3) 5^th root of square of 264.
(4) Cube of cube root of 3.

Solution:

We know that ‘n^th root of m^th power of a’ is expressed as (a^m)^1/n.

And ‘m^th power of n^th root of a’ is expressed as (a^1/n) ^m.

So by using the above rules let us find

(1) Square root of 5^th power of 121.

Square root of 5^th power of 121 is expressed as (121⁵)^1/2 or (121)^5/2.

(2) Cube of 4^th root of 324.

Cube of 4^th root of 324 is expressed as (324^1/4)³ or (324)^3/4.

(3) 5^th root of square of 264.

5^th root of square of 264 is expressed as (264²)^1/5 or (264)^2/5.

(4) Cube of cube root of 3.

Cube of cube root of 3 is expressed as (3^1/3)³ or (31)^3/3.

Practice set 3.3 PAGE NO: 18

1. Find the cube root of the following numbers.

(1) 8000

(2) 729

(3) 343

(4) -512

(5) -2744

(6) 32768

Solution:

(1) 8000

Firstly let us find the factor of 8000

8000 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5

So to find the cube root, we pair the prime factors in 3’s.

8000 = (2 × 2 × 5)³

= (2 × 10)³

= 20³

Hence, cube root of 8000 = ∛(8000)

= (20³)^1/3

= 20

(2) 729

Firstly let us find the factor of 729

729 = 9 × 9 × 9

So to find the cube root, we pair the prime factors in 3’s.

729 = 9³

Hence, cube root of 729 = ∛(729)

= (9³)^1/3

= 9

(3) 343

Firstly let us find the factor of 343

343 = 7 × 7 × 7

So to find the cube root, we pair the prime factors in 3’s.

343 = 7³

Hence, cube root of 343 = ∛(343)

= (7³)^1/3

= 7

(4) -512

Firstly let us find the factor of -512

-512 = (-8) × (-8) × (-8)

So to find the cube root, we pair the prime factors in 3’s.

-512 = (-8)³

Hence, cube root of -512 = ∛(-512)

= (-8³)^1/3

= -8

(5) -2744

Firstly let us find the factor of -2744

-2744 = (-14) × (-14) × (-14)

So to find the cube root, we pair the prime factors in 3’s.

-2744 = (-14)³

Hence, cube root of -2744 = ∛(-2744)

= (-14³)^1/3

= -14

(6) 32768

Firstly let us find the factor of 32768

32768 = 32 × 32 × 32

So to find the cube root, we pair the prime factors in 3’s.

32768 = 32³

Hence, cube root of 32768 = ∛(32768)

= (32³)^1/3

= 32

2. Simplify:

Solution:

Cube roots are used in day to day Mathematics, such as in powers and exponents or to find the side of a three-dimensional cube when its volume is given. Here, many such exercise problems are given, students can practice the solutions to secure good marks in the exams. Students can depend on these Solutions to understand all the topics under this chapter completely. Stay tuned to learn more about Indices and Cube Root, MSBSHSE Exam pattern and other information.