Surds & Indices Practice Set - Fully Solved

Q 1.(27)2/3=x then 3x is equal to
a) 6 b) 3 c) 27 d)9 e) None  


Q 2. ( 27/125 )-2/3 = ? 
a) 625/18 b) 25/9 c) 81/625 e) 9/25

Q 3. If (64)2/3 × (256)-1/2 = 4, then n= ?
a) 2 b) 4 c) 0 d) 1 e) None

Q 4.(64)0.25 × (36)1.5= ?
a) None b) 108 c) 48 d) 54 e) 1021

Q 5. 3√1000000/6√1000000=(100)x , then x is equal to .
a) 4 b) 1/2 c) None of these d) 1/4 e) 2

Q 6. (-1/1331)-2/3× √1331 × (1/121)3/2 
a) (1/11)-1/2 b) (-1/11)1/3 c) (-1/11)2/3 d) (-1/121)2/3 e) 113/2

Q7.(64/729)-1/3 = ?
a) -4/9 b) 8/9 c) 8/27 d) 21/4 e) None of these

Q 8. Simplify [x2n-1 + y2n-1]2[x2n-1 - y2n-1] .
a) x2n+ y2n b) x2n c) -y2n d) x2n- y2n e) None of these

Q 9. Arrange 22-1 , 4 0.33 , 60.25 in ascending order .
a)1st<2nd<3 b)3rd<2nd<1 c)1st<3rd<2 d)3rd<1st<2 e) None of these

Q 10. Evaluate (0.04)-1.5× (0.125)-4/3- (1/121)-1/2 
a) 1989 b) 22000 c) 2045 d) 2011 e) 2000 1/11

Q 11. Express 2/3 √32 as a pure surd .
a)√128 b)√128/9 c)√9/128 d) e) None of these

Solution

(1)
Sol: Option (c)
(27)2/3 = x ⇒ (33)2/3 = x ⇒ 32 = x ⇒ 3x = 2

(2)
Sol: Option (b)
(27/125)-2/3 = (125/27)2/3 = 25/9

(3)
Sol :Option (c)
(43)2/3×(44)-1/2 = 4n
4× 4-2 = 4n, ⇒40⇒ n = 0

(4)
Sol : Option (a)
(√642)1/3=(64)1/3=(43)1/3 = 4

(5)
Sol : Option (b)
3√1003/6√100= (100)⇒ 1001/2 = (100)x⇒ x = 1/2

(6) 
Sol: Option (a)
Convert each term to the base of 11
(-1/1331)-2/3 = (-1331)2/3 = (-11)3*2/3 = (-11)2 = 112
√1331 = 113/2 , (1/121)3/2 = 11-2*3/2 = 11-3

(7)
Sol: Option (d)
(43/93)-1/3
= (4/9)-1
9/4
= 21/4


(8)
Sol : Option (d)

Given expression = ( a+b ) ( a-b ) = a2 - b2
= [x2n-1 ]2 - [y2n-1]2
= x2n-1×21 - y2n-1×21
= x2n- y2n

(9)
Sol : Option (c)
(21/2) , (4 1/3) , (6 1/4
Here, the base and the index both are different .For comparision, either the base should be same or indices of each number should be same. Take LCM of 2,3,4 = 12 and convert each number to same index
(21/2) = (26)1/12 (44)1/12 ; (63)1/4
= (64)1/12 = (256)1/12 = (216)1/12
Clearly,(64)1/12 < (216)1/12 < (256)1/12  ⇒21/2< 60.25< 40.33

(10)
Sol : Option (a)
Given expression = (0.2)-3×(0.5)-4 - 11 = (0.2)-3×(0.5)-3.(0.5)-1-11
= (0.1)-3×(0.5)-1-11 = 2000-11

(11)
Sol : Option (b)
2/√32 = √(2/3)2×32
=√128/9 a pure surd


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