Railways Notes / Mathematics (Quantitative Aptitude) / Chapter 25
Chapter 25 of 31

Square Root & Cube Root

Finding square and cube roots quickly, plus the perfect square/cube reference tables worth memorising.

📖 ~4 min read 📐 RRB NTPC / Group D — Mathematics

Perfect Squares (1-20)

nn²nn²
1-101,4,9,16,25,36,49,64,81,10011-20121,144,169,196,225,256,289,324,361,400

Perfect Cubes (1-10)

nn³
1-101, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Finding Square Root by Division Method

  • Pair digits from the right; find the largest number whose square ≤ first pair
  • Bring down the next pair, double the quotient so far, find the next digit
  • Repeat until all pairs are used

Estimation Shortcut

To estimate √n quickly, find the nearest perfect squares below and above n and interpolate.
💡 Example: ∛343 = 7 (since 7³ = 343)

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