CBSE FREAK

Vedic Mathematics provides various concise methods to solve different types of equations − both linear and quadratic! These methods are extremely useful, especially in those cases, where the conventional methods take a lot of time. These methods are derived from the “ Sunyam Samyasamuccaye Sutra ” of Vedic Mathematics. Let us first consider the equation ( x + a ) ( x + b) = ( x + c ) ( x + d ), where ab = cd , i.e., where the product of the constant terms on the Left Hand Side equals that on the Right Hand Side. Watch the following video to understand how to solve such an equation. Solved Examples Example 1: Solve ( x + 14) ( x + 2) = ( x + 28) ( x + 1) Solution: Here, 14 × 2 = 28 × 1 = 28 ⇒ x = 0 Example 2: Solve ( x + 21) ( x + 3) = ( x + 9) ( x + 7) Solution: Here, 21 × 3 = 9 × 7 = 63 ⇒ x = 0 Summary: If, in the equation ( x + a ) ( x+ b ) = ( x + c ) ( x + d ), ab = cd , then the root of the equation will be x = 0. Let us now consider the equation

1. Square Root of a Number The method of finding the square root of a number is based on the application of “ Dvandvayoga ” or Duplex. Calculation of “ Dvandvayoga ” (Duplex) is very important in calculating the square root of any number. Watch the following video to understand the method of calculating the Duplex of a number. Solved Examples Example 1: Calculate the Duplex of 2852 Solution: Pair the digits of the number as shown below Example 2: Calculate the Duplex of 93242 Solution: Pair the digits of the number as shown below In order to calculate the square root of a number, the following points should be kept in mind: An exact square cannot end in 2, 3, 7, and 8. A perfect square ending in 1 must have either 1 or 9 (compliment of 1 from base 10) as the last digit of the square root. If a perfect square ends in 4, then the square root can only end in either 2 or 8 (complimentary to each other). If a perfect square ends in either 5 or 0, then its square r

1. Finding Squares of Numbers Using General Method This method of squaring is based on a corollary of “ Nikhilam sutra” , which reads “ Yavdunam Tavdunikratya vargam cha yojayet ” and means “whatever the extent of its deficiency, lessen it further to that very extent; and also set up the square of its deficiency”. This method is very helpful in calculating squares of numbers close to 10, 100, 1000, etc. Three probable cases are possible: Case I: When the number is less than and close to 10 n (For example, 98 2 ) Case II: When the number is greater than and close to 10 n (For example, 1009 2 ) Case III: When the number is not close to 10 n (For example, 45 2 ) Watch the following video to understand case I, where the number is less than 10 n . Solved Examples Example 1: Calculate 97 2 Solution: Base = 100 Deficit = 100 − 97 = 3 3 2 = 09 … (1) 97 − 3 = 94 … (2) ∴97 2 = 9409 Example 2: Calculate 983 2 Solution: Base = 1000 Deficit = 1000 − 983 = 17