Question

Find the square of a number 65 using Vedic Mathematics
\[
  {\text{A}}{\text{. 4235}} \\
  {\text{B}}{\text{. 4335}} \\
  {\text{C}}{\text{. 4220}} \\
  {\text{D}}{\text{. None of the above}} \\
 \]

Answer 1

Hint- We can see the number has the unit digit 5, so we can use the Vedic method of squaring it will make it easier and faster. The Vedic Mathematic technique includes 16 formulae and 13 sub formulas, including the topic like geometry, algebra, arithmetic, etc. Vedic mathematics includes two technique-specific techniques and general technique. If a number whose square is to be found ends with 5 specific techniques is used where the unit digit of the number whose square is to be formed is squared and the ten places digit is multiplied with one greater to it.

Complete step by step solution:
Since the unit place of the number is 5, we will use the specific technique of Vedic Mathematics for determining the square:
In the number \[65\]
\[\left( 5 \right)\] is units digit and \[\left( 6 \right)\] is the tens digit
Square the unit digit number, \[{5^2} = 25\]
And for the tens digit, multiply the number with the number one greater to it, i.e., 7.
So, \[\left( 6 \right) \times \left( {6 + 1} \right) = 6 \times 7 = 42\]
Now, in the answer square of 5 becomes the unit and tens digit and \[6 \times 7\]becomes the hundreds digit
So we get \[\left( {6 \times 7} \right)\left| {{5^2} = 42\left| {25} \right. = 4225} \right.\].
Hence the square of \[{\left( {65} \right)^2} = 4225\]
Answer does not match with the first three options given; hence the answer will be none of the above.

Note:Alternatively, the square of a number can be found by multiplying the number twice. To check here in this question, \[{\left( {65} \right)^2} = 65 \times 65 = 4225\] . The general technique is applied to another number whose square is to be found.