VEDIC MATHS-99
VEDIC MATHS
By OMKAR TENDOLKAR
Hello friends,
This is post number 99 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Raising to Fourth and Higher Powers-III"
Reference:
We had already learn about "Method Of Finding Cubes" in our previous blogs. If you have missed my last blog then please visit "VEDIC MATHS-50" to "VEDIC MATHS-52".
We had already learn about "Raising to Fourth and Higher Powers-I" in our previous blogs. If you have missed my last blog then please visit "VEDIC MATHS-97".
We had already learn about "Raising to Fourth and Higher Powers-II" in our previous blogs. If you have missed my last blog then please visit "VEDIC MATHS-98".
Raising a Number to the Fourth Power:
Example:
1. Say we have to find (32)^4.
Here a is 3 and b is 2.
Step 1:
We raise a to the power of 4, which means (3)^4 = 81.
Step 2:
Our first line looks something like this:
81 54 36 24 16
Step 3:
We will now do the next step for the second line.
- 54 gets multiplied by 3 to become 162.
- 36 gets multiplied by 5 to become 180.
- 162 gets multiplied by 3 to become 72.
Our sum looks like this now:
81 54 36 24 16
162 180 72
Step 4:
In our final step, we start adding from right to left. Remember, each column will give us a single digit.
- From right to the left, we put down 6 and carry 1 to the next column.
- 24 + 72 + 1 (carried over) = 97. We put down 7 and carry 9 to the next column.
- 36 + 180 + 9 = 225. We put down 5 and carry 22 to the next column.
- 54 + 162 + 22 = 238. We put down 8 and carry over 23 to the next column.
- Finally, we have 81 + 23 = 104.
- Our answer is 1048576.
Our sum on completion looks like this:
81 54 36 24 16
162 180 72
-----------------------------
104 8 5 7 6
Answer:
(32)^4 = 1048576.
2. Say we have to find (51)^4.
Here a is 5 and b is 1.
Step 1:
We raise a to the power of 4, which means (5)^4 = 625.
Step 2:
We then multiply the subsequent digits by 1/5 as b/a is 1/5 = 1/5. So our first line looks like this:
625 125 25 5 1
Step 3:
We will now do the next step for the second line.
- 125 gets multiplied by 3 to become 375.
- 25 gets multiplied by 5 to become 125.
- 5 gets multiplied by 3 to become 15.
Our sum looks like this now:
625 125 25 5 1
375 125 15
Step 4:
In our final step, we start adding from right to left. Remember, each column will give us a single digit.
- We put down 1 in the unit’s place.
- In the ten’s place, we add 5 + 15 = 20. We put down 0 in the ten’s place and carry over 2 to the next step.
- In the hundred’s column, we have 25 + 125 + 2, this gives us 152. We put down 2 and carry over 15 to the next step.
- In the thousand’s place, we have 125 + 375 + 15 = 505. We put down 5 and carry 51 to the next step.
- In the final step, we have 625 +51 = 676.
- So our final answer is 6765201.
Our sum on completion looks like this:
625 125 25 5 1
375 125 15
-----------------------------
676 5 2 0 1
Answer:
(51)^4 = 6765201.
We can apply the same principles and raise the number to fifth and sixth powers as well. The method is the same, and I am sure you would like to try it out for yourself.
To get you started I am giving you the expansion of (a + b)^5 here.
(a + b)^5 = (a)^5 + 5(a)^4b + 10(a)^3(b)^2 + 10(a)^2(b)^3 + 5(a)(b)^4 + (b)^5
Solve the following example.
1. (34)^4
3. (95)^5
Ans : (34)^4 =1336336.
2. (53)^4
Ans : (53)^4 = 7890481.
Ans : (95)^5 = 7737809375.
The simplicity of this method can be vouched from examples given above.
You may try following examples.
1. (41)^4
2. (55)^4
3. (69)^4
4. (73)^5
5. (97)^5
In next blog we will discuss about "Applications of the Sutras & Sub-sutras".
Are you excited for this?...
Then, please wait for it.
I will post my new blog in next week.
We will meet very soon through our next blog. Till that stay connected, stay healthy and stay safe.
Thanks
for giving your valuable time.
Good day😊
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