Vedic Maths
Ancient calculation shortcuts for multiplication, squares, cubes, roots and checks
Nikhilam Multiplication
Multiply two numbers that are both just under 100 or 1000
Target 15s
Urdhva-Tiryakbhyam
Vertical-crosswise multiplication for any two 2-digit numbers
Target 20s
Squaring Near a Base
Square numbers close to 100 or 1000 in your head
Target 12s
Squaring Numbers Ending in 5
One of the most famous Vedic shortcuts — square any "n5" instantly
Target 6s
Multiply by 9, 99, 999...
Multiply a number by a run of nines without ever multiplying by 9
Target 10s
Same Start, Units Add to 10
A famous special case: e.g. 43 × 47 — both start with 4, and 3 + 7 = 10
Target 8s
Squaring Near 50
Square any number from 41 to 59 in one step
Target 8s
Cubing Near a Base (Yavadunam)
Cube numbers like 102 or 997 without long multiplication
Target 25s
Duplex Squaring Exam favourite
Square any 2-digit number with a² | 2ab | b²
Target 10s
Division by 9
Running digit sums give the quotient and the remainder
Target 15s
Working Base 50 (Anurupyena)
Multiply numbers near 50 using base 100 ÷ 2
Target 15s
Cube Root of a Perfect Cube Exam favourite
Find 2-digit cube roots instantly from the first and last digits
Target 10s
Square Root of a Perfect Square Exam favourite
Find 2-digit square roots from the last digit and a quick check
Target 12s
Both Numbers Above the Base
Nikhilam for numbers just over 100, like 104 × 107
Target 12s
One Above, One Below the Base
Multiply numbers on either side of 100, like 104 × 97
Target 15s
Subtraction from 100, 1000, 10000
"All from 9 and the last from 10"
Target 8s
Digit-Sum Check (Casting Out 9s) Exam favourite
Check a multiplication answer in seconds
Target 15s
Equations with Swapped Coefficients
Solve ax + by = c, bx + ay = d by adding and subtracting
Target 40s
Same Units, Tens Add to 10 Exam favourite
Multiply pairs like 47 × 67 in one line
Target 8s