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Square Roots & Surds

Quantitative Aptitude · Maths Bookwise · Number System

Useful for: SSC CGL

BOOK-GUIDED ORIGINAL SSC MATHS PRACTICE — Square Roots & Surds

FOUNDATION

(n + 1)² = n² + 2n + 1.

METHOD

Identify the quantities given, choose the exact relationship, calculate in the same unit, then check the answer against the question.

WORKED EXAMPLE 1

Find √(107² + 2 × 107 + 1).

By (n+1)²=n²+2n+1, the expression is √(108²)=108.

WORKED EXAMPLE 2

Find √(70² + 2 × 70 + 1).

By (n+1)²=n²+2n+1, the expression is √(71²)=71.

IMPORTANT EXCEPTION / COMMON TRAP

Square root denotes the principal nonnegative root.

QUICK REVISION

(n + 1)² = n² + 2n + 1.

SEE MORE: https://study.kundali-iq.com/ssc-maths/roots/

For complete timed maths practice, use SSC CGL Test Series → New Maths 100 Mixed Sets or Chapter-wise sets. These are independent original questions, not copied previous-year questions.

Practice MCQs

Find √(107² + 2 × 107 + 1).
1. 122
2. 115
3. 108
4. 101
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Show answer
Answer: (c) 108. By (n+1)²=n²+2n+1, the expression is √(108²)=108.
Find √(70² + 2 × 70 + 1).
1. 67
2. 71
3. 75
4. 79
Read chapter notes · Similar questions
Show answer
Answer: (b) 71. By (n+1)²=n²+2n+1, the expression is √(71²)=71.
Find √(101² + 2 × 101 + 1).
1. 102
2. 96
3. 108
4. 114
Read chapter notes · Similar questions
Show answer
Answer: (a) 102. By (n+1)²=n²+2n+1, the expression is √(102²)=102.
Find √(46² + 2 × 46 + 1).
1. 53
2. 44
3. 47
4. 50
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Show answer
Answer: (c) 47. By (n+1)²=n²+2n+1, the expression is √(47²)=47.
Simplify √50 ÷ √2
1. 2√5
2. 10
3. 5
4. 25
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Show answer
Answer: (c) 5. √50/√2 = √25 = 5 (using the principal square roots).

Square Roots & Surds

Practice MCQs

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