Quick method to evaluate polynomials – Horner’s method
This is a guest post by Nandeesh H.N. of Kolkata
How to find the value of a Polynomial Function?
Horner's method is commonly used to find the roots of a polynomial function. However it can also be used to evaluate the polynomial function for a given value of x.
Suppose, we want to evaluate the polynomial
p(x) = 4x^5 - 3x^4 + 7x^3 + 6x^2 + 3x + 9 at x = 2.41.
The usual method of evaluation is to evaluate each product (such as 4*2.41^5 or 7*2.41^3) separately and then add. The drawback is that to evaluate any power of x, we go through all of the previous powers.
A slightly better method is to make a table of powers of 2.41 and put them in the given polynomial.
Popularity: 40%
Shortcut to Find Square of a Number
Today I will discuss a very simple method of finding square of numbers between 26 to 74 mentally. In the subsequent post we will cover higher numbers. So keep watching this space to learn squaring any number within your mind
Square (also called perfect square) is an integer that is the square of an integer; in other words, it is the product of some integer with itself. So, for example, 9 is a square number, since it can be written as 3 × 3.
How to find the square of any number?
To apply this method you should know squares of 1 to 25 by heart. You can refer to this table to learn the same.
Popularity: 76%
Quick calculations for extremely large numbers
A guest post by Nandeesh H.N. of Kolkata
Quick calculations with a few logarithms
If you can remember a few logarithms, you can do many calculations quite easily without the aid of calculators or computers.
Try to remember the logarithms of just seven numbers:
Log 2 = 0.30, log 3 = 0.48, log 7 = 0.85, log 11= 1.04, log 13= 1.11, log 17 = 1.23 and log 19=1.28.
The logarithm of a composite number is equal to the sum of the logarithms of its prime factors; you can formulate the following table of logarithms:
Popularity: 55%
Shortcut Method for Multiplication
A guest post by Nandeesh H.N. of Kolkata
Shortcut multiplication for approximate numbers
When applying the rules of multiplication of exact numbers to approximate numbers we waste time and effort in the computation of digits that will be dropped at a later stage. The computation can be made more efficient if we are guided by the following rules:
Popularity: 73%
Herons Method of Finding Roots
A guest post by Nandeesh H.N. of Kolkata
"Dear Vineet,
I am really grateful to you for your blog which makes Mathematics a pleasure. Keep up your good work. As requested by you I am sending a brief note on Heron’s method of finding square root. This method can be easily extended to find any root.
Heron’s method of finding square root
Popularity: 65%
Find Day of the Week on Any Date
Lots of time we are in a situation where we are supposed to know the day on a particular date of the current year. Most of the methods you will come across are not mentally possible for everyone and hence not feasible. So find below a practical Quicker Maths method of finding what day of the week will be on a particular date.
Find the day on any date of current year
I have come across a very simple way to find the day of the week for any date of the current year. This idea is so easy, that most of you will wonder why you didn't think of it yourselves.
All you have to do is........
Popularity: 53%
Finding Cube Root – Vedic Maths Way
This is an amazing trick which was always appreciated by the audience I have addressed in various workshops. This awe inspiring technique helps you find out the cube root of a 4 or 5 or 6 digits number mentally.
Before going further on the method to find the cube root, please make a note of the following points –
1) Cube of a 2-digit number will have at max 6 digits (99^3 = 970,299). That implies if you are given with a 6 digit number, its cube root will have 2 digits.
2) This trick works only for perfect cubes, it will not work for any arbitrary 6-digit
3) It works only for integers
Popularity: 100%
Fast Multiplication Tricks
Simple Fast Multiplication Tricks & Techniques
Fast Multiplication by 5: Multiply by 10 (just place 0 after the original number) and divide the result by 2.
Fast Multiplication by 6: Sometimes subsequent multiplication by 3 and then 2 is easy.
Fast Multiplication by 9: Multiply by 10 (just place 0 after the original number) and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number, as above.
Multiply by 16: You can double four times, if you want to. Or you can multiply by 8 and then by 2.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 18: Multiply by 20 and subtract twice the original number (which is obvious from the first step).
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number (which is obvious from the first step).
Multiply by 45: Multiply by 50 and subtract 5 times the original number (which is obvious from the first step).
Multiply by 90: Multiply by 9 (as above) and put a zero on the right.
Multiply by 98: Multiply by 100 (just place 00 after the original number)and subtract twice the original number.
Multiply by 99: Multiply by 100 (just place 00 after the original number)and subtract the original number.
Did you liked the above fast multiplication tricks ?
Please leave a comment below, that will help us to improve
Popularity: 52%
Vedic Multiplication of two numbers close to Hundred
Vedic Method of Multiplication: Base System of multiplication
Application: Multiplication of two numbers close to Hundred
Case 1: Both numbers greater than 100.
Example of vedic multiplication using above method
• 103 x 104 = 10712
The answer is in two parts: 107 and 12,
107 is just 103 + 4 (or 104 + 3), and 12 is just 3 x 4.
• Similarly 107 x 106 = 11342
107 + 6 = 113 and 7 x 6 = 42
123 x 103 = 12669
(123 + 3) | (23 x 3) = 126 | 69 =12669 .
If the multiplication of the offsets is more than 100 then this method won’t work. For example 123 x 105. Here offsets are 23 and 5.
Multiplication of 23 and 5 is 115 which are more than 100. So this method won’t work.
But it can still work with a little modification. Consider the following examples:
Example 1
122 x 123 = 15006
Step 1: 22 x 23 = 506 (as done earlier)
Step 2: 122 + 23 (as done earlier)
Step 3: Add the 5 (digit at 100s place) of 506 to step 2
Answer: (122 + 23 + 5) | (22 x 23) = 150 | 06 = 10506
Example 2
123 x 105 (Different representation but same method)
123 + 5 = 128
23 x 5 = 115
128 | 115
= 12915
In the next post we will tell you about vedic multiplication, i.e., how to multiply two numbers lesser than the base (in this case 100)
If you liked this method of vedic multiplication included in ancient Vedic Maths, Please leave a comment to let us know.
Popularity: 32%
Shortcut to find the Cube of a number
Very often we have to find the cube, i.e. third power of 2 digit numbers. Cubes of very large numbers are rarely used.
Cubes of all the single digits should be memorized. Find below the table of cubes of first ten natural numbers -
13 = 1, 23 = 8, 33 = 27, 43 = 64, 53 = 125,
63 = 216, 73 = 343, 83 = 512, 93 = 729, 103 = 1000
To find the cube of any 2 digit number, we have to take the following steps
First Step: The first thing we have to do is to put down the cube of the tens-digit in a row of 4 figures. The other three numbers in the row of answer should be written in a geometrical ratio in the exact proportion which is there between the digits of the given number.
Second Step: The second step is to put down, under the second and third numbers, just two times of second and third number. Then add up the two rows.
Finding the cube of 12
Or, 123 = ?
First Step: Digit in ten’s place is 1, so we write the cube of 1. And also as the ratio between 1 and 2 is 1:2, the next digits will be double the previous one. So, the first row is
1 2 4 8
Step II: In the above row our 2nd and 3rd digits (from right) are 4 and 2 respectively. So, we write down 8 and 4 below 4 and 2 respectively. Then add up the two rows.
Ex 2: 163 = ?
Soln:
Explanations: 13 (from 16) = 1. So, 1 is our first digit in the first row. Digits of 16 are in the ratio 1:6, hence our other digits should be 1×6 = 6, 6×6 = 36, 36×6 = 216. In the second row, double the 2nd and 3rd number is written. In the third row, we have to write down only one digit below each column (except under the last column which may have more than one digit). So, after putting down the unit-digit, we carry over the rest to add up with the left-hand column. Here,
i) Write down 6 of 216 and carry over 21.
ii) 36 + 72 + 21 (carried) = 129, write down 9 and carry over 12.
iii) 6 + 12 + 12 (carried) = 30, write down 0 and carry over 3.
iv) 1 + 3 (carried) = 4, write down 4.
Popularity: 54%
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