Nikhilam Navatascaramam Dastah (Nikhilam Sutra)
Shortcut method of multiplication using Vedic Mathematics when numbers are closer to power of 10 (10,100,1000,…)
निखिलं नवतस्चरमं दशतः
All from 9 and last from 10.
Stuff you need to know before starting:
Before starting with Nikhilam Sutra Multiplication, I recommend you to go through the 2.Vinculum Process. (Vinculum Process will be used in Type 3 of Nikhilam Tecnique)
Specific Condition Required:
Numbers need to be close* to power of 10 (10, 100, 1000, etc).
Also Read => More Vedic Mathematics Sutras for Multiplication.
- Depending upon the numbers closer to power of 10, we select that power of 10 as our Base.
- Apply the principle of Nikhilam i.e. subtract the digits from Base – All the digits from 9 and last from 10. (write besides those numbers) (See below example 94 * 96). Those numbers if positive will be called as exceses and if negative will be called as deficiencies.
- Multiply those deficiencies or excesses. (write in 2nd compartment).
- Do Cross Addition of Numbers with deficiencies or excesses. (write in 1st Compartment)
- 2nd compartment ALWAYS needs to have same number of digits as that of zeroes of the selected Base. If less then pre-append zeroes. If more, carry forward initial digits to 1st compartment
- Below Examples will clear the process. Nikhilam Sutra can be classified in 3 groups as follows:
Nikhilam Type 1:
This type of Nikhilam Sutra can be applied when numbers slightly* less than power of 10 (10, 100, 1000, etc.).
Formula used: (x-a)(x-b) = x(x-a-b) + ab
Nikhilam Type 2:
Numbers slightly* greater than power of 10 (10, 100, 1000, etc.).
Formula used:(x+a)(x+b) = x(x+a+b) + ab
Nikhilam Type 3:
- (x+a)(x-b) = x(x+a-b) – ab
- (x-a)(x+b) = x(x-a+b) – ab
Nikhilam Multiplication Tips (*):
If we observe above multiplication of 998 and 1123, even though numbers are NOT very close to power of 10 but still we can easily manage to apply Nikhilam Method. This is because we ALSO have to take consideration of multiplication of excessive/deficiency with the number. If multiplication of them is easily manageable then we can apply Nikhilam Method.
Restating Specific Condition Required (*):
Numbers need NOT to be close to power of 10 BUT multiplication of excess/deficiency with the numbers should be manageable. But if numbers are closer to power of 10 then we can surely apply any of the Nikhilam Method.
What You Think ????
Which of the following examples should be solved using Nikhilam Sutra and which should not be and why ?? (Lets see how many of you understood the Nikhilam Sutra:))
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