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 and the value of 8 + 232 – 3128 + 450 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
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.

4
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.

5
If 3 = 1.732 is given. then the value of

2 + √3  = ?
2 – √3
» Explain it
B
Given expression =  
2 +  3
 
2 –  3

=  
(2 +  3
)(
2 +  3
)
 
(2 –  3
)(
2 +  3
)

[On rationalising the denominator]

=  
  (
2 +  3
)2
 = 
(2 +  3 )2
4 – 3

= 22 + ( 3 )2 + 2 × 2 ×  3

= 4 + 3 + 4  3

= 7 + 4 × 1.732

= 7 + 6.928 = 13.928

Hence, option B is correct.