Square & Cube Roots
Square Roots & Cube Roots
Square and cube root questions reward pure memorization: commit squares up to 30 and cubes up to 20 to muscle memory. Last-digit patterns let you eliminate wrong MCQ options instantly without full calculation. SSC CGL Tier 1 and Tier 2 both test direct root computation, and these values reappear inside mensuration, Pythagorean triplet, and simplification problems.
Key Idea
Memorise squares up to 30 and cubes up to 20. Last digit patterns let you instantly eliminate wrong answers in MCQs without full calculation.
Core Formulas
Square root property
√(a×b) = √a × √b; √(a/b) = √a / √b
Break a complex root into simpler parts or combine two roots into one product.
Simplify surd
√(n²×m) = n√m — factor out largest perfect square
Extract the largest perfect-square factor to reduce a surd to its simplest form.
Last digit of perfect square
Units digit of n determines units digit of n²; only 0,1,4,5,6,9 can be last digits of perfect squares
To check if a number can be a perfect square
Cube root last digit
Last digit of cube = same as last digit of cube root (except 2↔8, 3↔7)
To find last digit of cube root
Approx square root
√N ≈ nearby perfect square root ± (difference)/(2 × nearby root)
Quick estimation of square roots
Relevant Exams
Direct square root and cube root questions in SSC CGL Tier 1 and 2. Also used in simplification, mensuration (side from area), and Pythagorean triplet identification.