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Squaring a number ending with 5(mentally)

here is an easy way to find the square of any number ending with 5.

firstly,the last two digits of your answer will always be 25..it is always common..

for eg, 25^2=625..last two digits 25..

then the first digit(s) of the square will be the product of the first digit of the number (for eg, in my above eg, it is 2) and the number just after it( in 25^2, 1st digit=2..number just after it=3)

2*3_25

625

Note by Yoogottam Khandelwal
1 year, 8 months ago

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This also works with 2 digit numbers where tens digit is same and the sum of unit digits is 10.

for eg,

7476=(78)_6*4

=5624 Yoogottam Khandelwal · 1 year, 8 months ago

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@Yoogottam Khandelwal Very nice observation too! Indeed both unit digits are 5, is a special case of sum of unit digits is 10. Calvin Lin Staff · 1 year, 8 months ago

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Good observation. Do you know why it works? Calvin Lin Staff · 1 year, 8 months ago

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@Calvin Lin Yes..i know..

let the number be x5 where x is any number (1,2,3..9)

but, x5 is represented numerically as 10*x+5

now, when we square x5,

(10*x+5)^2

=(100*x^2)+(2 * 5 * 10 * x)+25

=(100 * x^2)+(100 * x)+25

=100(x^2+x)+25

=100 * x * (x+1)+25

so, the square of x5 is x * (x+1)_25 Yoogottam Khandelwal · 1 year, 8 months ago

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