Square of a Number Ending in 5 (Indian Method)

Square integers ending in 5 such as 35 or 65 using the Indian (Vedic) mental math trick. It breaks down each step: multiply the tens part by the next number, then append 25.

Input

Enter an integer ending in 5 to compute its square with the Indian mental math method and see the steps broken down.

Integer ending in 5

Enter a positive integer ending in 5, such as 5, 15, 35, or 105.

Result

Square of 35

1,225

Front part

Back part

Square

1,225

Upper part h

Next number h+1

h times (h+1)

How to do it in your head

Drop the final 5 of 35 to get the upper part h = 3.

Multiply h by the next number. 3 times 4 equals 12, which is the front part.

Always append 25 as the back part.

Join the back part 25 after the front part 12 to get the square 1,225.

A number N ending in 5 is N = 10h + 5, and N squared equals 100 times h times (h+1) plus 25.

How it works

An integer N ending in 5 can be written as N=10h+5, where h is the part above the ones digit.
Then N squared equals 100 times h times (h+1) plus 25. Put h times (h+1) in front and append 25 to get the square.
For example, with 35 you get h=3 and 3 times 4 equals 12, so appending 25 gives 1225.
For 75, h=7 and 7 times 8 equals 56, append 25 to get 5625. For 105, h=10 and 10 times 11 equals 110, append 25 to get 11025.
Numbers that do not end in 5, or values of 5 or below, are out of range. Because you only multiply the upper part by the next number, you can do it quickly in your head.

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