Home » Quantitative Aptitude » Algebra » Surds and Indices Level 1 » all » Surds and Indices Quiz 4

Direction: Study the following questions carefully and choose the right answer.
1
Given  2  = 1.414. The value of   8  + 2  32  – 3  128  + 4  50  is

» Explain it
A
8  + 2  32  – 3  128  + 4 50  

=  2  2  + 8  2  – 3 × 8  2  + 4 × 5  2  

=  (2 + 8 – 24 + 20)  2  

=  6  2  = 6 × 1.414 = 8.484

Hence, option A is correct.

2
The simplified value of ( 3  + 1)(10 +   12 )( 12  – 2)(5 –   3 ) is

A
16
» Explain it
C
Expression =  ( 3  + 1)(10 +  12 )( 12  – 2)(5 –  3 ) 

= ( 3  + 1)(10 + 2  3 )(2  3  – 2)(5 –  3 ) 

= ( 3  + 1) × 2(5 +  3 ) × 2( 3  – 1)(5 –  3 ) 

= 4( 3  + 1)( 3  – 1)(5 –  3 )(5 +  3 )  

= 4(3 – 1) (25 – 3)                                [(a + b)(a – b) = a2 – b2]

= 4 × 2 × 22 = 176.

Hence, option C is correct.

3

A
» Explain it
B


Hence, option B is correct.

4
If 
15
 = 3.88, then what is the value of 
5
3
 

» Explain it
A
Given, 
15
 = 3.88

Now,  
5
3
 = 
5 × 3
3 × 3
 = 
15
 
3

=   3.88  = 1.293
3

Hence, option A is correct.

5
Simplify:  (6.25)1/2 × (0.0144)1/2 + 1  
(0.027)1/3 × (81)1/4

» Explain it
D
Expression:   (6.25)1/2 × (0.0144)1/2 + 1  
(0.027)1/3 × (81)1/4

=  (2.5)2×(1/2) × (0.12)2×(1/2) + 1  
(0.3)3×1/3 × (3)4×(1/4)

=  2.5 × 0.12 + 1  =  0.3 + 1
(0.3) × (3) 0.9

=   1.3  = 1.4444 = 1.4
0.9

Hence option D is correct.