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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 + 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
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 / 3 = 1.293

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) × (3) = (0.3 + 1) / 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 / 4 – 3 = (2 + √3)2

= 22 + (√3)2 + 2 × 2 × √3

= 4 + 3 + 4√3

7 + 4 × 1.732

= 7 + 6.928 = 13.928

Hence, option B is correct.