Question

To find the square of 45 by ekadhikena purvena method the digit 4 should be multiplied by which number.
A. by its previous number
B. by zero
C. by its next number
D. by ten

Answer 1

Hint: Ekadhikena purvena method is a method derived from vedic maths. It is an ancient form of maths that enlists tricks and tips to perform long calculations. It makes us aware of the magic with numbers. It is always fun to learn vedic maths and these methods have been discovered by our ancestors.

Complete step-by-step answer:
Let us now understand this method, it is used to find the square of the number without performing actual long multiplication.
Following are the steps involved while finding square of a two digit number with the help of ekadhikena purvena method:
We have the number 45 for which we have to find the square, therefore the digit at ten’s place is multiplied with the number obtained by adding one to the digit present at ten’s place. In this case the digit at ten’s place is 4 and the number obtained by adding one to it is (4+1) i.e 5. Therefore we will get $4 \times 5 = 20$ .
Now the digit at one’s place is 5, it will be squared
$
  \Rightarrow 4\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{5} = {5^2} \\
  \Rightarrow 5 \times 5 = 25 \;
$
Therefore we get the final multiplied result from step 1 and 2 by,
$
  \mathop 4\limits_ \downarrow {5^2}\Rightarrow {5^2} = 25 \\
  (4 \times (4 + 1)) = 4 \times 5 = 20 \\
  \Rightarrow 2025 \;
$
Therefore
$\Rightarrow {45^2} = 2025$
Hence we can conclude that the correct option is C.
So, the correct answer is “Option C”.

Note: We must note that ekadhikena purvena is only applicable to numbers ending with the digit 5. One can find the square of two and three digit numbers as well from this method. In the above case one must not get confused that the digit is multiplied with the number next to it. If the number would have been 35, 3 would have been multiplied with 4.