SQUARE and SQUARE ROOT SHORTCUTS |
SQUARE & SQUARE ROOT SHORTCUTS
1
Squaring Numbers Ending in 5
Multiply the leading digit by the next consecutive number, then write 25 at the end.
Example: 85²
1. First digit: 8
2. Next number: 9 (8 × 9 = 72)
3. Append 25: 7225
Answer = 7,225
2
Base 50 Square Shortcut
Compare number to 50. Add/subtract difference from 25 for the first half, and square the difference for the last half.
Example: 53²
1. Difference from 50 is +3
2. First half: 25 + 3 = 28
3. Last half: 3² = 09
Answer = 2,809
3
Base 100 Square Shortcut
Add the difference from 100 to the number itself, and square the difference for the suffix.
Example: 96²
1. Difference from 100 is -4
2. First part: 96 - 4 = 92
3. Last part: (-4)² = 16
Answer = 9,216
4
Using (a+b)(a-b) = a² - b²
Find squares by shifting to an easier nearby round number.
Example: 49²
1. View as (50 - 1)²
2. 50² - 2(50)(1) + 1²
3. 2500 - 100 + 1 = 2401
Answer = 2,401
5
Any 2-Digit Square (a², 2ab, b²)
Square digits left and right, and put twice their product in the middle with carries.
Example: 43²
1. Left: 4² = 16
2. Middle: 2 × (4 × 3) = 24
3. Right: 3² = 9
Answer = 1,849
6
Fast Square Root Estimation
Find nearest lower square root and adjust using the linear approximation formula.
Example: √115
1. Nearest root below is √100 = 10
2. Formula: Root + (Diff ÷ (2 × Root))
3. 10 + (15 ÷ 20) = 10.75
Approx = 10.72