SSC CGL Elementary Surds with 30 exam-oriented questions, detailed solutions, shortcuts, and Tier-I & Tier-II practice for faster and more accurate preparation.
SSC CGL Elementary Surds
1. Simplify 
A) 6√3 B) 7√3
C) 8√3 D) 9√3
Correct Answer: A) 6√3
Explanation:
2. Rationalise the denominator:
A) √7 + √2 B) √7 – √2
C)√2 – √ 7 D) √5
Correct Answer: B) √7 – √2
Explanation:
= √7 – √2
3. Find the value of:
A) 8 + 2√15 B) 8 + √15
C) 2 + 2√15 D) 8 – 2√15
Correct Answer: A) 8 + 2√15
Explanation:
(a + b)2= a2 + b2 + 2ab
= 8 + 2√15
4. Simplify: 
A) 2 B) 12
C) √2 D) 24
Correct Answer: A) 2
Explanation:
(a + b)(a – b)=a2 – b2
7– 5 = 2
5. If x = √7 + √6 then the value of x + 1/x is
A) 2 √7 B) 2 √6
C) √7 + √6 D) 7+ √6
Correct Answer: A) 2 √7
Explanation:
x = √7 + √6
= √7 – √6
x + 1/x = √7 + √6 + √7 – √6
= 2√7
6 Evaluate: 
A) √3 + √2 B) √3 – √2
C) 1 D) √6– 1
Correct Answer: B) √3 – √2
Explanation:
= √3 – √2
7. Simplify: 
A) 3√2 B) 4√2
C) 5√2 D) 3√2
Correct Answer: B) 4√2
Explanation:
SSC CGL Elementary Surds
8. If a= √5 + √2 and b=√5 – √2, then the value of ab is
A) 3 B) 5
C) 7 D) √3
Correct Answer: A) 3
Explanation:
ab = (√5 – √2)( √5 – √2)
= (√5)2 – (√2)2
= 5 – 2 = 3
9. Find: (√2 + 1) (√2 – 1)
A) 0 B) 1
C) 2 D) √2
Correct Answer: B) 1
Explanation:
(√2 + 1) (√2 – 1)= (√2)2 – 12
=2–1
=1
10. Simplify: 
A) (3 + √5)/2 B) (5 + √5)/2
C) 3 + √5 D) 2 + √5
Correct Answer: A) (3 + √5)/2
Explanation:
= (3 + √5)/2
SSC CGL Elementary Surds
11. If x= √3 + √2, then find x2
A) 5 + √6 B) 5+2√6
C) 6 + √5 D) (5 – 2√6)
Correct Answer: B) 5+2√6
Explanation:
x= √3 + √2
x2= (√3 + √2)2
= 3 + 2 + 2√6
= 5 + 2√6
12 Evaluate: (√3+ √2)2– (√3 – √2)2
A) 2√6 B) 4√6
C) 6√2 D) 10
Correct Answer: B) 4√6
Explanation:
Use:(a + b)2– (a – b)2=4ab
a=√3, b=√2
(√3+ √2)2– (√3 – √2)2 = 4√3 × √2
=4√6
13 Simplify: √(12) ×√(27)
A) 9 B) 12
C) 18 D) 36
Correct Answer: C) 18
Explanation:
√(12) ×√(27) = √(12 × 27)
= √(324)=18
14 Find the value of: frac(√6)/(√3)
A) √2 B) 2
C) √3 D) 3
Correct Answer: A) √2
Explanation:
(√6)/(√3)
=√(6/3)
=√2
SSC CGL Elementary Surds
15. If x=√2+√3, then find: x2 – 2√6.
A) 2 B) 3
C) 5 D) 6
Correct Answer: C) 5
Explanation:
x2 = (√2 + √3)2
= 2 + 3 + 2√6
= 5 + 2√6
x2 – 2√6 = 5
16. Rationalise: 3/(2+√3)
A) 6 – 3√3 B) 6 + 3√3
C) 3 – √3 D) 2 – √3
Correct Answer: A) 6 – 3√3
Explanation:
3/(2+√3) = [3/(2+√3)][ (2 – √3/(2+√3)]
= [3(2–√3)]/(4–3)
=6 – 3√3
17. Find: (√5 + √3)(√5 + √3)
A) 8 + 2√(15) B) 8 + √(15)
C) 2 + 2√(15) D) 5 + 3√(15)
Correct Answer: A) 8+2√(15)
Explanation:
(√5+√3)2 = 5 + 3 + 2√(15)
=8 + 2√(15)
18. Which of the following is a rational number?
A) √2 + √3 B) √5 – √2
C) √7×√7 D) √3 + √6
Correct Answer: C) √7×√7
Explanation:
√7×√7 =7
Which is rational.
The other expressions remain irrational.
19 Simplify: 1/(√5 – √3)
A) (√5+√3)/2 B) √5 + √3
C) (√5 – √3)/2 D) 2
Correct Answer: A) (√5+√3)/2
Explanation:
1/(√5–√3) = [1/(√5–√3)] × (√5+√3)/(√5+√3)
= (√5+√3)/(5–3)
= (√5 + √3)/2
20. If a=√3+√2, then find a – 1/a
A) (√3+√2)/2 B) (√3+√2)
C) 2√3 D) 2√2
Correct Answer: D) 2√2
Explanation:
1/a =1/(√3+√2)
=√3 – √2
a – 1/a = (√3 + √2) – (√3 – √2)
=2√2
SSC CGL Elementary Surds
21. Evaluate: (√7 + √2)2 + (√7 – √2)2
A) 14 B) 18
C) 20 D) 56
Correct Answer: C) 18
Explanation:
(a + b)2+ (a – b)2=2(a2 + b2)
(√7 + √2)2 + (√7 – √2)2 = 2[(√7)2 + (√2)2]
2(7 + 2)=18
22. Simplify: [√8 + √(18)]/(√2)
A) 3 B) 5
C) 7 D) 5√2
Correct Answer: B) 5
Explanation:
√8 = 2√2 and √(18) = 3√2
[√8 + √(18)]/(√2) = [2√2 + 3√2)]/√2
= (5√2)/(√2)=5
23. If x=√5 – √2, then x2 is:
A) 7– 2√(10) B) 3 – 2√(10)
C) 7 + 2√(10) D) 3+2√(10)
Correct Answer: B) 7 – 2√(10)
Explanation:
x2 = (√5 – √2)2
= 5 + 2 – 2√(10)
=7–2√(10)
24 Find the value of: (√6 + √5)(√6 – √5)
A) 1 B) 11
C) 0 D) 30
Correct Answer: A) 1
Explanation:
(√6)2– (√5)2 = 6 – 5 = 1
SSC CGL Elementary Surds
25 Simplify: √(45)+√(20) – √5
A) 3√5 B) 4√5
C) 5√5 D) 6√5
Correct Answer: B) 4√5
Explanation:
√(45)=3√5 and √(20)=2√5
√(45)+√(20) – √5 = 3√5 + 2√5 – √5
=4√5
26. If √x = 3 + √2, then find x
A) 11+6√2 B) 11+3√2
C) 9 + 2√2 D) 7+6√2
Correct Answer: A) 11+6√2
Explanation:
√x = 3 + √2
Square both sides
x = (3 + √2)2
= 9 + 2 + 6√2
=11 + 6√2
27. Evaluate: 1/(3+√8)
A) 3 – √8 B) 3+ √8
C) 3 D) √8
Correct Answer: D) A
Explanation:
(3 + √8)(3 – √8) = 9 – 8
= 1
1/(3+√8)= 3 – √8
28. Simplify: (√2 + √3)(√3 – √2)
A) 1 B) √6 – 2
C) 2√6 – 1 D) 5
Correct Answer: A) 1
Explanation:
(√2 + √3)(√3 – √2) = √2√3 – √2√2 + √3√3 – √3√2
=√6 – 2 + 3 – √6
=1
29. Find the value of: [√(12)]/(√3 + √2)
A) 6 + 2√6 B) √3 + √2
C) 6 – 2√6 D) √3 – √2
Correct Answer: C) 6 – 2√6
Explanation:
√(12)=2√3
(2√3)/ (√3+√2) = [2√3 × (√3 – √2)]/(3 – 2)
=2√3(√3 – √2)
=6 – 2√6
30. If x = √2 + √3, find: x4 – 10x2
A) 1 B) –1
C) 0 D) 10
Correct Answer: B) –1
Explanation:
x2 = (√2+√3)2
=5 + 2√6
x4 = (5+2√6)2
= 25 + 24 + 20√6
=49 + 20√6
10x2 = 50 + 20√6
x4 – 10x2 = (49 + 20√6) – (50 + 20√6)
= –1
SSC CGL Elementary Surds
SSC CGL Quantitative Aptitude Topics
- Number System
- Decimals
- Fractions
- Percentages
- Ratio & proportion
- Square roots
- Averages
- Interest (simple & compound)
- Profit & loss
- Discount
- Partnerships
- Mixture & Alligation
- Time & speed & distance
- Time & work.
- Advanced math includes basic algebraic identities
- Elementary surds
- Graphs of linear equations
- Triangles
- Circles
- Regular polygons, right prisms, cones, cylinders, spheres
- Trigonometry.
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