Question

Using the Sutra Sankalana Vyavakalan, find the square of
A) 23
B) 38
C) 69

Answer 1

Hint: In Vedik mathematics the square of a number can be calculated by using Sutra Sankalana Vyavakalan formula. As we know that ${a^2} = ({a^2} - {b^2}) + {b^2}$. As we know that ${a^2} - {b^2} = (a - b)(a + b)$ so the equation can be further simplified as ${a^2} = (a - b)(a + b) + {b^2}$. We can write number 23 as $23 = 20 + 3$, \[38 = 40 - 2\] and $69 = 70 - 1$. Using the formula we can calculate the square of the number.

Complete step-by-step answer:
Here we have to find the square of the number using the Sutra Sankalana Vyavakalan. It is a method used in Vedik mathematics for finding the square of a number.
In this method we use the basic formula like ${a^2} = ({a^2} - {b^2}) + {b^2}$. As we that ${a^2} - {b^2} = (a - b)(a + b)$, so equation can be further simplified as ${a^2} = (a - b)(a + b) + {b^2}$.
We have to write numbers in a form whose squares can be easily remembered.
Now doing the squares of the numbers one by one
A) 23
Here the given number is 23. Number 23 can be represented as $23 = 20 + 3$. We can also write as $23 = 30 - 7$. Answers will be the same for all cases.
So, here for number 23, $a = 23$ and $b = 3$
Using the formula ${a^2} = (a - b)(a + b) + {b^2}$
Putting the values of a and b,
${23^2} = (23 - 3)(23 + 3) + {3^2}$
So, ${23^2} = (20)(26) + 9$,
Simplifying, ${23^2} = 520 + 9$
So, ${23^2} = 529$.
So, the square of the number 23 is 529.
B) 38
Here the given number is 38. Number 38 can be represented as $38 = 40 - 2$. We can also write as $38 = 30 + 8$. Answers will be the same for all cases.
So, here for number 38, $a = 38$ and $b = - 2$
Using the formula ${a^2} = (a - b)(a + b) + {b^2}$
Putting the values of a and b,
${38^2} = (38 - ( - 2)(38 + ( - 2)) + {( - 2)^2}$
So, \[{38^2} = (38 + 2)(38 - 2) + 4\],
So, ${38^2} = (40)(36) + 4$
Simplifying, ${38^2} = 1440 + 4$
So, ${38^2} = 1444$.
So, the square of the number 38 is 1444.
C) 69
Here the given number is 69. Number 69 can be represented as $69 = 70 - 1$. We can also write as $69 = 60 + 9$. Answers will be the same for all cases.
So, here for number 69, $a = 69$ and $b = - 1$
Using the formula ${a^2} = (a - b)(a + b) + {b^2}$
Putting the values of a and b,
${69^2} = (69 - ( - 1)(69 + ( - 1)) + {( - 1)^2}$
So, \[{69^2} = (69 + 1)(69 - 1) + 1\],
So, ${69^2} = (70)(68) + 1$
Simplifying, ${69^2} = 4760 + 1$
So, ${69^2} = 4761$.
So, square number 69 is 4761.

Note: In Vedik mathematics there are three methods for squaring a number which are Yavadunam, Ekadhikina Purvena and Dwandwa yoga. Yavadunam is used for squares of numbers which are close to the power of 10 i.e. 10, 100, 1000… Ekadhikena Purvena method is used for squares of a number which has a last digit as 5. While Dwandwa yoga is the general method used for squaring any number.