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Brilliant’s Composite Mathematics Class 8 Solutions Chapter 3 Exponents and Radicals
Welcome to NCTB Solutions. Here with this post we are going to help 8th class students for the Solutions of Brilliant’s Composite Mathematics Class 8 Math Book, Chapter 3, Exponents and Radicals. Here students can easily find step by step solutions of all the problems for Exponents and Radicals, Exercise 3.3, 3.2, 3.3, 3.4 and 3.5 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily.
Exponents and Radicals Exercise 3.1 all Questions Solution
Question no – (1)
Solution :
(i) -4 seventh power
= (-4)7
(ii) 2/6 eight power
= (2/6)8
(iii) 3/7 zeroth power
= (3/7)6
(iv) 10 fifth power
= (10)5
(v) 1/3 fourth power.
= (1/3)4
Question no – (2)
Solution :
(i) x3/x7
= x-4
(ii) 52 × 53
= 52 + 3
= 55
(iii) (-5)2 × (- 5)-2
= (- 5)2 – 2
= (-5)0
= 1
(iv) (1/3)5 . (1/3)2
= (1/3)5+2
= (1/3)7
(v) (2a3/b4)3
= 8a0/b12
(vi) (216)0
= 1
(vii) (23)6
= 2 3×6
= 218
(viii) (- a3 b2)5
= – a15b10
Question no – (3)
Solution :
(i) 60 or 8-1
∴ 60 = 1 and 8– 1= 1/8.
Clearly, 60 > 8-1
(ii) 32 or 31/2
∴ 32 = 9 and 31/2
= √3= 1.732.
Clearly, 32 > 31/2
(iii) 34 or 43
∴ 34 = 81 and 43 – 64.
Clearly, 34 > 43
(iv) (3)6 or (1/3)6
∴ (3)6 = 729 and (1/3)6 = 1/729,
Clearly, (3)6 > (1/3)6
(v) 7– 2 or 7– 1.
∴ 7 – 2 = 1/72 = 1/49 and 77 = 1/7 = 7/49.
Clearly, 7 -2 < 7 -1
Exponents and Radicals Exercise 3.2 all Questions Solution
Question no – (1)
Solution :
(i) 91/2
= 2√9
(ii) (- 1/3)1/6
= 6√-1/3
(iii) (19)1/3
= 3√19
(iv) (17/19)17/23
= 17/23√17/19
(v) (64/625)2/3
= 2/3√64/625
Question no – (2)
Solution :
| No. | (i) | (ii) | (iii) | (iv) | (v) |
| Radicand | -2 | 7.01 | 35 | -1/5 | 9 |
| Index | 5 | 3 | 5 | 5 | 7 |
Question no – (3)
Solution :
(i) 5√25
= 25 × 1/5
= 21
= 2
∴ The value will be 2
(ii) (3√- 3)3
= (- 3)3 × 1/3
= – 31
= – 31
= – 3
∴ The value will be -3
(iii) √62
= 61/2×2
= 61
= 6
∴ The value will be 6
(iv) (10√7)7
= 77/10
∴ The value will be 77/10
(v) √(- 27)3
= (- 27)3 ×1/2
= (- 27)3/2
∴ The value will be (- 27)3/2
Exponents and Radicals Exercise 3.3 all Questions Solution
Question no – (1)
Solution :
(i) 3√27
= (27)1/3
(ii) 5√392
= 392/5
(iii) 5√(125)3
= (125)3/5
(iv) 8√(2/3)2
= (2/3)1/4
(v) 3√2– 6
= 2– 2
(vi) 5√8/9
= (8/9)1/5
(vii) 3√29– 7
= 29– 7/3
(viii) 10√(10)– 2.
= (10)– 1/5
Question no – (2)
Solution :
(i) (2)1/5
= 5√2
(ii) (25)2/5
= 5√(25)2
(iii) (- 216)3/5
= 5√(- 216)2
(iv) (- 29)7/3
= 3√(- 29)7
(v) (5/17)1/9
= 9√5/17)
(vi) (- 64)4/7
= 7√(- 64)4
(vii) 193/7
= 5√(19)3
(viii) (1.01)5/7
= 7√(101)5
Question no – (3)
Solution :
(i) (16)-1/2
= 1/(16)1/2
= 1/√16
= 1/4
(ii) (625)3/4
= (4√625)3
= (5)3
= 125
(iii) 100– 3/2
= 1/(100)3/2
= 1/(√100)3
=1/(10)3
= 1/1000
(iv) 4/36– 1/2
= 4 × (36)1/2
= 4 × (√36)
= 4 × 6
= 24
(v) (25/9)– 1/2
= (9/25)1/2
= √9/√25
= 3/5
(vi) (64/169)– 1/2
= (169/64)1/2
= √169/√64
= 138.
= 13/18
(vii) (512/729)2/3
= (512)2/3/(729)2/3
= (3√512)2/(3√729)2
= (8)2/(9)2
= 64/81
Question no – (4)
Solution :
(i) 151/2 × 151/2
= 151/2 + 1/2
= 151
= 15 …(Simplified)
(ii) 811/3 × 5761/3
= 3√81 × 3√576
= 3√81 × 576
= 3√3 × 3 × 3 × 3 × 3 × 3 × 4 × 4 × 4
= 3 × 3 × 4
= 36 …(Simplified)
(iii) 64-2/3 × 27-2/3
= 1/(64)2/3 × 1/(27)2/3
= 1/(3√64)2 × 1/(√27)2
= 1/(4)2 × 1/(3)2
= 1/16 × 1/9
= 1/144 …(Simplified)
(iv) 5122/3 × 5121/3 × 512– 4/3
= 512(2/3 + 1/3 – 4/3)
= 512 -1/3
= 1/(512)1/3
= 1/8 …(Simplified)
(v) 3 × 643/2 × 64– 1/2
= 3 × (64)3/2 – 1/2
= 3 × (64)2/2
= 3 × 64
= 192 …(Simplified)
Question no – (5)
Solution :
(i) 165/2 ÷ 161/2
= 16(5/2 – 1/2)
= 164/2
= 162
= 256 …(Simplified)
(ii) 154/3 ÷ 152/3
15(4/3 – 2/3)
= 152/3 …(Simplified)
(iii) ((64)2/3)1/2
= (64)2/3 × 1/2
= (64)1/3
= 4 …(Simplified)
(iv) (1510)0
= 1 …(Simplified)
(v) [(625)1/2]2
= (625)1/2 ×2
= 625 …(Simplified)
(vi) (510)-1/10
= (5)10 × – 1/10
= (5)– 1
= 1/5 …(Simplified)
(vii) 134/3 ÷ 131/3
= 134/3 – 1/3
= 131
= 13 …(Simplified)
(viii) 54/3 × 52/3
= 54/3 + 2/3
= 56/3
= 52
= 25 …(Simplified)
Question no – (6)
Solution :
(i) x-7 × y-7
= (xy)-7 ….(Simplified)
(ii) x-3/x3.
= x-1 (Simplified)
(iii) x5/7 ÷ x12/7
= x(5/7 – 12/7)
= x -7/7
= x– 1
= 1/x …(Simplified)
(iv) x0 – y0/x0 + y0
= 1 – 1/1 + 1
= 0/2
= 0 …(Simplified)
(v) (x3 y4 z-6)0
= 1 …(Simplified)
Question no – (7)
Solution :
(i) (82/3)-3/2
= (8)2/3 × – 3/2
= (3)– 1
= 1/8
(ii) (81/16)– 1/4
= (16/81)1/4
= 4√16/4√81
= 2/3
(iii) (0.027)2/3
= (3√0.0027)2
= (0.3)2
= 0.09
(iv) (0.04)3/2
= (√0.04)3
= (0.2)3
= 0.008
(v) (16/625)1/4
= 4√16/4√625
= 2/5
(vi) (512/1728)-2/3
= (1728/512)2/3
= (3√1728)2/(3√512)2
= (12/8)2
= (3/2)2
= 9/4
Question no – (8)
Solution :
(i) 49-2 × 251/2/6-1
= 251/2 × 61/492
= √25 × 6/2401
= 5 × 6/2401
(ii) 641/2 × (641/2 + 1
= √64 × (√64 + 1)
= 8 × (8 +1)
= 8 × 9
= 72
(iii) 367/2 – 369/2/365/2
= (√36)7 – (√36)9/(√36)5
= 67– 69/65
= 65(62 – 64)/65
= 62 – 64
= 36 – 1296
= – 1260
(iv) (13 + 23 + 33)1/2
= (1 + 8 + 27)1/2
= (36)1/2
= √36
= 6
(v) (52 + 122) 1/2
= (25 + 144)1/2
= (169)1/2
= 13
(vi)√b3/a × √b/a
= √b3 × b/a × a
= √b4/a2
= b2/a
Question no – (9)
Solution :
(i) 64 × (1/82)3 = 8n
Given, 64 × (1/82)3 = 8n
Or, (8)2 × 1/(8)6
= 8n
∴ (8)2 – 6
= 89
∴ The value of n will be 89
(ii) 512 × (1/83)3 = 83n
∴ (8)3 × 1/(8)9 = 83n
Or, (8)(3 – 9) = 83n
Or, 8 -6 = 83n
Or, – 6 = 3n
∴ n = – 2
∴ Therefore, the value of n will be – 2
Exponents and Radicals Exercise 3.5 all Questions Solution
Question no – (1)
Solution :
(i) 7√7
(ii) 5/√5
(v) √17/15
These radicals are in the simplest form.
Question no – (2)
Solution :
(vi) √3/1 – √5
= 3(1 + √5)/(1 – √5)91 + √5)
= 3(1 + √5)/1 – (√5)2
= 3 + 3√5/1 – 5
= -(3 + 3√5)/4
(viii) √8 – √75/√8 + √75
= (√8 – √75)( √8 – √75)/ (√8 + √75)( √8 + √75)
= 8 + 75 – 2√8√75/(8 – 75)
= 83 – 2 √600/- 67
= 83 – 20√6/- 67
= 20√6 – 83/67
(ix) √2 – 1/√2 + 1
= (√2 – 1)( √2 – 1)/( √2 + 1)( √2 – 1)
= 2 + 1 – 2√2/2 – 1
= 3 – 2√2/1
= 3 – 2√2
(xi) 6/4 – √10
= 6(4 +m √10)/(4 – √10)(4 + √10)
= 6(4 +√10)/16 – 10
= 6(4 + √10)/6
= (4 + √10)
(xii) √3 + √2/√3 – √2
= (√3 + √2)( √3 + √2)/( √3 – √2)( √3 + √2)
= 3 + 2 + 2√3√2/3 – 2
= 5 + 2√6/1
= 5 + 2√6
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