Class 8 MAHARASHTRA STATE TEXTBOOK BUREAU Solutions Maths Chapter 3: Indices and Cube root
Indices and Cube root Exercise Ex. 3.1
Solution 1(1)
Fifth root of 13 comparing with nth root of a if 
Hence, n = 5 and a = 13
Index form is 
Solution 1(2)
Sixth root of 9 comparing with nth root of a if
Hence, n = 6 and a = 9
Index form is 
Solution 1(3)
Square root of 256 comparing with nth root of a if
Hence, n = 2 and a = 256
Index form is 
Solution 1(4)
Cube root of 17 comparing with nth root of a if
Hence, n = 3 and a = 17
Index form is 
Solution 1(5)
Eighth root of 100 comparing with nth root of a if
Hence, n = 8 and a = 100
Index form is 
Solution 1(6)
Seventh root of 30 comparing with nth root of a if
Hence, n = 7 and a = 30
Index form is 
Solution 2(1)
comparing with nth root of a if
Hence, n = 4 and a = 81
It is said as 4th root of 81.
Solution 2(2)
comparing with nth root of a if
Hence, n = 2 and a = 49
It is said as square root of 49.
Solution 2(3)
comparing with nth root of a if
Hence, n = 5 and a = 15
It is said as 5th root of 15.
Solution 2(4)
comparing with nth root of a if
Hence, n = 9 and a = 512
It is said as 9th root of 512.
Solution 2(5)
comparing with nth root of a if
Hence, n = 19 and a = 100
It is said as 19th root of 100.
Solution 2(6)
comparing with nth root of a if
Hence, n = 7 and a = 6
It is said as 7th root of 6.
Indices and Cube root Exercise Ex. 3.2
Solution 1(1)
Consider, 
= (
Cube of square root of 225
Consider, = (
Square root of cube of 225
Solution 1(2)
Consider, 
= (
4th power of 5th root of 45
Consider, 
= (
5th root of 4th power of 45
Solution 1(3)
Consider, 
= (
6th power of 7th root of 81
Consider, = (
7th root of 6th power of 81
Solution 1(4)
Consider, 
= (
4th power of 10th root of 100
Consider, = (
10th root of 4th power of 100
Solution 1(5)
Consider, 
=
Cube of 7th root of 21
Consider, = 
7th root of cube of 21
Solution 2(1)
5th power of 121 is 1215.
Square root of 5th power of 121 is 
Solution 2(2)
4th root of 324 is 
.
Cube of 4th
root of 324 is 
Solution 2(3)
Square of 264 is 2642.
5th root of square of 264 is 
Solution 2(4)
Cube root of 3 is 
.
Cube of cube root of 3 is 
Indices and Cube root Exercise Ex. 3.3
Solution 1(1)
= ?
Consider,
8000 = 8 × 1000
= 23 × 103
= (2 × 10)3 = 203
Hence, = 20
Solution 1(2)
= ?
Consider,
729 = 9 × 81
= 9 × 9 × 9
= 93
Hence, = 9
Solution 1(3)
= ?
Consider,
343 = 7 × 49
= 7 × 7 × 7
= 73
Hence, = 7
Solution 1(4)
= ?
Consider,
-512 = -1 × 8 × 64
= -1 × 8 × 8 × 8
= -13 × 83
Hence, = ‒8
Solution 1(5)
= ?
Consider,
-2744 = -1 × 7 × 392
=-1 × 7 × 7 × 56
= -1 × 7 × 7 × 7 × 8
= -13 × 73 × 23
= (-1 × 7 × 2)3
= -143
Hence, = ‒14
Solution 1(6)
= ?
Consider,
32768 = 4 × 8192
= 4 × 4 × 2048
= 4 × 4 × 4 × 512
= 4 × 4 × 4 × 4 × 128
= 4 × 4 × 4 × 4 × 4 × 32
= 4 × 4 × 4 × 4 × 4 × 4 × 8
= 43 × 43 × 23
= (4 × 4 × 2)3
= 323
Hence, = 32
Solution 2(1)
=
= 
Solution 2(2)
=
=
= 
Solution 2(3)
Consider,
=
= 
= 
= 0.09