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}Â root of â€˜aâ€™ 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 â€˜n^{th}Â root of aâ€™ in each of the following numbers.
Solution:
In general, a^{1/n}Â is written as â€˜n^{th}Â root of aâ€™.
So now,
(1) (81)^{1/4}
(81)^{1/4}Â is written as â€˜4^{th}Â root of 81â€™.
(2) (49)^{1/2}
(49)^{1/2}Â is written as â€˜square root of 49â€™.
(3) (15)^{1/5}
(15)^{1/5}Â is written as â€˜5^{th}Â root of 15â€™.
(4) (512)^{1/9}
(512)^{1/9}Â is written as â€˜9^{th}Â root of 512â€™.
(5) (100)^{1/19}
(100)^{1/19}Â is written as â€˜19^{th}Â root of 100â€™.
(6) (6)^{1/7}
(6)^{1/7}Â is written as â€˜7^{th}Â root of 6â€™.
Practice set 3.2 PAGE NO: 16
1. Complete the following table.
Sr. No. |
Number |
Power of the root |
Root of the power |
(1) |
(225)^{3/2} |
Cube of square root of 225 |
Square root of cube of 225 |
(2) |
(45)^{4/5} |
||
(3) |
(81)^{6/7} |
||
(4) |
(100)^{4/10} |
||
(5) |
(21)^{3/7} |
Solution:
GenerallyÂ we can express the number a^{m/n} as
a^{m/n}Â = (a^{m})^{1/n}Â means â€˜n^{th}Â root of m^{th}Â power of aâ€™.
a^{m/n}Â = (a^{1/n})^{m}Â means â€˜m^{th}Â power of n^{th}Â root of aâ€™.
So by using the above rules let us fill the table:
Sr. No. |
Number |
Power of the root |
Root of the power |
(1) |
(225)^{3/2} |
Cube of square root of 225 |
Square root of cube of 225 |
(2) |
(45)^{4/5} |
Fourth power of fifth root of 45 |
Fifth root of fourth power of 45 |
(3) |
(81)^{6/7} |
Sixth power of seventh root of 81 |
Seventh root of sixth power of 81 |
(4) |
(100)^{4/10} |
Fourth power of tenth root of 100 |
Tenth root of fourth power of 100 |
(5) |
(21)^{3/7} |
Cube of seventh root of 21 |
Seventh root of cube of 21 |
2. Write the following number in the form of rational indices.
(1) Square root of 5^{th}Â power of 121.
(2) Cube of 4^{th}Â root of 324.
(3) 5^{th}Â root of square of 264.
(4) Cube of cube root of 3.
Solution:
We know that â€˜n^{th}Â root of m^{th}Â power of aâ€™ is expressed as (a^{m})^{1/n}.
And â€˜m^{th}Â power of n^{th}Â root of aâ€™ is expressed as (a^{1/n})^{ m}.
So by using the above rules let us find
(1) Square root of 5^{th}Â power of 121.
Square root of 5^{th}Â power of 121 is expressed as (121^{5})^{1/2}Â or (121)^{5/2}.
(2) Cube of 4^{th}Â root of 324.
Cube of 4^{th}Â root of 324 is expressed as (324^{1/4})^{3}Â or (324)^{3/4}.
(3) 5^{th}Â root of square of 264.
5^{th}Â root of square of 264 is expressed as (264^{2})^{1/5}Â or (264)^{2/5}.
(4) Cube of cube root of 3.
Cube of cube root of 3 is expressed as (3^{1/3})^{3}Â 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 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 5 Ã— 5 Ã— 5
So to find the cube root, we pair the prime factors in 3â€™s.
8000 = (2 Ã— 2 Ã— 5)^{3}
= (2 Ã— 10)^{3}
= 20^{3}
Hence, cube root of 8000 = âˆ›(8000)
= (20^{3})^{1/3}Â
= 20
(2) 729
Firstly let us find the factor of 729
729 = 9 Ã— 9 Ã— 9
So to find the cube root, we pair the prime factors in 3â€™s.
729 = 9^{3}
Hence, cube root of 729 = âˆ›(729)
= (9^{3})^{1/3}Â
= 9
(3) 343
Firstly let us find the factor of 343
343 = 7 Ã— 7 Ã— 7
So to find the cube root, we pair the prime factors in 3â€™s.
343 = 7^{3}
Hence, cube root of 343 =Â âˆ›(343)
= (7^{3})^{1/3}
= 7
(4) -512
Firstly let us find the factor of -512
-512 = (-8) Ã— (-8) Ã— (-8)
So to find the cube root, we pair the prime factors in 3â€™s.
-512 = (-8)^{3}
Hence, cube root of -512 =Â âˆ›(-512)
= (-8^{3})^{1/3}Â
= -8
(5) -2744
Firstly let us find the factor of -2744
-2744 = (-14) Ã— (-14) Ã— (-14)
So to find the cube root, we pair the prime factors in 3â€™s.
-2744 = (-14)^{3}
Hence, cube root of -2744 = âˆ›(-2744)
= (-14^{3})^{1/3}Â
= -14
(6) 32768
Firstly let us find the factor of 32768
32768 = 32 Ã— 32 Ã— 32
So to find the cube root, we pair the prime factors in 3â€™s.
32768 = 32^{3}
Hence, cube root of 32768 =Â âˆ›(32768)
= (32^{3})^{1/3}Â
= 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.