Vedic Math Sutra: Sutra 2-Nikhilam Navatashcaramam Dashatah

This blog will discuss Sutra 2: the Nikhilam Navatashcaraman Dashatah, which can quickly multiply numbers close to a base number.

This sutra is often translated as “All from 9 and the last from 10.”

Recommended Reading: Vedic Math Sutras: Sutra 1-Ekadhikena Purvena

Here are the steps to apply the sutra:

1. Identify a base number close to the numbers you want to multiply. It is usually chosen as a power of 10 or a multiple of 10 for simplicity.
2. Subtract each digit from the base number. If the digit is greater than the base number, subtract it from the next higher multiple of the base number.
3. Cross subtraction of left numbers with the right. 
4. Multiplication of the right numbers
   
5. Write down the product obtained in Step 3 as the Left part of the answer and Step 4 as the Right side of the number
6. Combine the left and right parts to get the final answer.

Example

Here’s an example to illustrate the sutra:

Let’s say we want to multiply 96 and 98.

Step 1: Choose a base number close to these two numbers. Let’s choose 100 as the base.

Step 2: Subtract each digit from 100:

For 96 -100 = -4

For 98-100 = – 2 

Step 3: Cross subtraction of Left numbers 

Left   Right

Step 4: Multiplication of the right side numbers

Left   Right

The right number should also be two digits, so instead of 8, we will write 08

Step 5: Put the Left number first and then the Right Number

Right number 94 

Left Number 08

Step 6: Combine the two numbers, and you will get your answer

Answer: 9408

Therefore, using the “Nikhilam Navatashcaraman Dashatah ” sutra, we can quickly find that 96 multiplied by 98 equals 9408.

Recommended Reading: 16 SUTRAS OF VEDIC MATH

The next one will be Urdhava – Tiryagbyham.

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