Question

Find the square of $225$ using Vedic Mathematics.
A. $125625$
B. $125655$
C. $105625$
D. None of these

Answer 1

Hint: Firstly, we will break the given value into two parts .We will multiply 25 by the $25$.Thereafter we will multiply 2 by 25 and then put together to get the answer.


Complete step by step solution:
Step-1: We will break 225 into two parts:$2/25$
So, deviation is $25$.
Left side of the answer is to multiply the number and deviation.
Then, left side of the answer $ = 2.25 = 50$
Step 2: The right side of the answer has two digits and that can be obtained by taking the square of the deviation.
Then, right side of the answer $ = {(25)^2} = 625$
Hence, from the obtained number$625$, added to the left side.
Then, the left side becomes $50 + 625 = 50625$
Therefore, the answer is $50625$.
Hence, the correct option is D.


Note: This method is useful for finding the square number. Students must add a hundredth place of $50$and the unit place of $625$ to get the desired result. We can find square of 225 by another method:
\[{\left( {225} \right)^2} = n\left( {n + 1} \right)/25\]
Here, \[
  n = 22, \\
  and n + 1 = 22 + 1 = 23 \\
 \]
$
  {\left( {225} \right)^2} = 22X23/25 \\
  {\left( {225} \right)^2} = 506/25 \\
  {\left( {225} \right)^2} = 50625 \\
 $