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Page No 15:

Question 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:

It is known that,

nth root of a is expressed as a1/n.

(1) Fifth root of 13

= (13)1/5

(2) Sixth root of 9

= (9)1/6

(3) Square root of 256

= (256)1/2

(4) Cube root of 17

= (17)1/3

(5) Eighth root of 100

= (100)1/8

(6) Seventh root of 30

= (30)1/7

Page No 15:

Question 2:

Write in the form 'nth root of a' in each of the following numbers.
(1) 8114

(2) 4912

(3) 1515

(4) 51219

(5) 100119

(6) 617

Answer:

It is known that,

nth root of a is expressed as a1/n.
1 8114
= Fourth root of 81
2 4912
= Square root of 49
3 1515
= Fifth root of 15
4 51219
= Ninth root of 512
5 100119
= Nineteenth root of 100
6 617
= Seventh root of 6



Page No 16:

Question 1:

Complete the following table.

Sr. No. Number Power of the root Root of the power
(1) 22532 Cube of square root of 225 Square root of cube of 225
(2) 4545    
(3) 8167    
(4) 100410    
(5) 2137    

Answer:

 

Sr. No. Number Power of the root Root of the power
(1) 22532 cube of square root of 225 square root of cube of 225
(2) 4545 4th power of 5th root of 45 5th root of 4th power of 45
(3) 8167 6th power of 7th root of 81 7th root of 6th power of 81
(4) 100410 4th power of 10th root of 100 10th root of 4th power of 100
(5) 2137 cube of 7th root of 21 7th root of cube of 21

Page No 16:

Question 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:

It is known that,

am/n = (am)1/n means 'nth root of mth power of a'.

am/n = (a1/n)m means 'mth power of nth root of a'.

(1) Square root of 5th power of 121
=121512=12152
(2) Cube of 4th root of 324
=324143=32434
(3) 5th root of square of 264
=264215=26425
(4) Cube of cube root of 3
=3133=333



Page No 18:

Question 1:

Find the cube roots of the following numbers.
(1) 8000
(2) 729
(3) 343
(4) −512
(5) −2744
(6) 32768

Answer:

(1) To find the cube root of 8000, let us factorise 8000 first.
8000=2×2×2×2×2×2×5×5×58000=4×4×4×5×5×5 = 43×53=4×53    am×bm=a×bm8000=20380003=20
(2) To find the cube root of 729, let us factorise 729 first.
729=3×3×3×3×3×3729=3×3×3×3×3×3=3×33=937293=9
(3) To find the cube root of 343, let us factorise 343 first.
343=7×7×7=733433=7
(4) To find the cube root of  −512, let us factorise 512 first.
512=2×2×2×2×2×2×2×2×2512=2×2×2×2×2×2×2×2×2=8×8×8×=83-512=-8×-8×-8=-83-5123=-8
(5) To find the cube root of −2744, let us factorise 2744 first.
2744=2×2×2×7×7×72744=2×7×2×7×2×7=2×73=143-2744=-143-27443=-14
(6) To find the cube root of 32768, let us factorise 32768 first.
32768=2×2×2×2×2×2×2×2×2×2×2×2×2×2×232768=2×2×2×2×2×2×2×2×2×2×2×2×2×2×2=32×32×32=323327683=32

Page No 18:

Question 2:

Simplify:
(1) 271253

(2) 16543

Answer:


1 271253=3×3×35×5×53=33533=3533     ambm=abm=35
2 16543=2×2×2×22×3×3×33=2×2×23×3×33=23333=2333    ambm=abm=23

Page No 18:

Question 3:

If 7293 = 9 then 0.0007293 = ?

Answer:

It is given that,
7293=90.0007293=72910000003=729310000003=93310033=9100=0.09
 



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