class 8: maths : Indices and Cube root: All Practice Set

 class 8: maths: Indices and Cube root:Practice Set:3.1

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

ANSWER :

i. (13)15
ii. (9)16
iii. (256)12
iv. (17)13
v. (100)18
vi. (30)17

2. Write in the form ‘nth root of a’ in each of the following numbers.

i. (81)14
ii. (49)12
iii. (15)15
iv. (512)19
v. (100)119
vi. (6)17
ANSWER :
i. Fourth root of 81.
ii. Square root of 49.
iii. Fifth root of 15.
iv. Ninth root of 512.
v. Nineteenth root of 100.
vi. Seventh root of 6.

Extra Questions and Activities

Question 1.
Using laws of indices, write proper numbers in the following boxes. (Textbook pg, no. 14)
i. 35×32=3()
ii. 37÷39=3()
iii. (34)5=3()
iv. 5−3=15()
v. 50=()
vi. 51=()
vii. (5×7)2=5()×7()
viii. (57)3=()3()3
ix. (57)−3=(()())3
Solution:
i. 35×32=37
ii. 37÷39=3−2
iii. (34)5=320
iv. 5−3=153
v. 50=1
vi. 51=5
vii. (5×7)2=52×72
viii. (57)3=5373
ix. (57)−3=(75)3

 class 8: maths : Indices and Cube root :Practice Set :3.2

Practice Set :3.2

1. Complete the following table.

S.No.	Number	Power of the root	Root of the power
1.	(225)32	Cube of square root of 225	Square root of cube of 225
2.	(45)45
3.	(81)67
4.	(100)410
5.	(21)37

ANSWER :

S.No.	Number	Power of the root	Root of the power
1.	(225)32	Cube of square root of 225	Square root of cube of 225
2.	(45)45	4th power of 5th root of 45	5th root of 4th power of 45
3.	(81)67	6th power of 7th root of 81	7th root of 6th power of 81
4.	(100)410	4th power of 10th root of 100	10th root of 4th power of 100
5.	(21)37	Cube of 7th root of 21	7th root of cube of 21

2. Write the following numbers in the form of rational indices. 

 (1) Square root of 5th power of 121. 

(2) Cube of 4th root of 324 

 (3) 5th root of square of 264 

(4) Cube of cube root of 3

ANSWER :

i. (121)52
ii. (324)34
iii. (264)25
iv. (3)33

 class 8: maths : Indices and Cube root :Practice Set :3.3

Practice Set :3.3

1. Find the cube roots of the following numbers. 

(1) 8000 

(2) 729 

(3) 343 

(4) -512 

(5) -2744 

(6) 32768

ANSWER :

i. 8000
= 2 × 2 × 2 × 10 × 10 × 10
= (2 × 10) × (2 × 10) × (2 × 10)
= (2 × 10)³
= 20³

ii. 729

= (3 × 3) × (3 × 3) × (3 × 3)
= (3 × 3)³
= 9³

iii. 343
= 7 × 7 × 7
= 7³

iv. -512
= 2 × 2 × 2 × 4 × 4 × 4
= (2 × 4) × (2 × 4) × (2 × 4)
= (2 × 4)³
= 8³
∴ – 512 = (- 8) × (- 8) × (- 8)
= (-8)³

v. -2744
= 2 × 2 × 2 × 7 × 7 × 7
= (2 × 7) × (2 × 7) × (2 × 7)
= (2 × 7)³
= 14³
∴ -2744 = (-14) × (-14) × (-14)
= (-14)³

vi. 32768
= 2 × 2 × 2 × 4 × 4 × 4 × 4 × 4 × 4
= (2 × 4 × 4) × (2 × 4 × 4) × (2 × 4 × 4)
= (2 × 4 × 4)³
= 32³

2 .Simplify:
i. 27125−−−√3
ii. 1654−−√3
iii. If 729−−−√3=9 then 0.000729−−−−−−−√3 = ?

ANSWER :
(1) 27125−−−√3=3×3×35×5×5−−−−−√3=3353−−√3=(35)3−−−−√3     [ambm=(ab)m]=35$\left(\mathrm{<br>},\mathrm{<br>},\mathrm{<br>},\mathrm{<br> }\right)$

(2) 1654−−√3=2×2×2×22×3×3×3−−−−−−−√3=2×2×23×3×3−−−−−√3=2333−−√3=(23)3−−−−√3    [ambm=(ab)m]=23

(3) It is given that,

729−−−√3=90.000729−−−−−−−√3=7291000000−−−−−√3=729√31000000√3=93√3(100)3√3=9100=0.09

Chapter 3 : Indices and Cube root

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