Question

the possible units digit in √676​

Answer 1

Answer:

Note:

[1] The square of largest 1 digit number being 81 and the square of smallest 3 digit number being 10000, the square root of 676 has to be a 2 digit number.

let the two digits of the square root be expressed as 10 x+ y ,

(10x+y)^2= 100x^2 +20xy +y^2

The contribution to the unit digit comes only from y^2,

y has to be 4 or 6

[2] The above arguments hold for a number with any number of digits.

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