VEDIC MATHS-98
VEDIC MATHS
By OMKAR TENDOLKAR
Hello friends,
This is post number 98 from the series of "Vedic maths" blogs. Here in this blog we will learn about "Raising to Fourth and Higher Powers-II"
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".
Raising a Number to the Fourth Power:
Example:
1. Say we have to find (13)^4.
Here a is 1 and b is 3.
Step 1:
We raise a to the power of 4, which means (1)^4 = 1. This 1 is the first digit. We put it down like this: 1.
Step 2:
We then multiply the subsequent digits by 3 as b/a is 3/1 = 3. So our first line looks like this:
1 3 9 27 81
Step 3:
We will now do the next step for the second line.
- 3 gets multiplied by 3 to become 9.
- 9 gets multiplied by 5 to become 45.
- 27 gets multiplied by 3 to become 81.
Our sum looks like this now:
1 3 9 27 81
9 45 81
Step 4:
In our final step, we start adding from right to left. Remember, each column will give us a single digit.
- From 81 we put down 1 in the unit’s place and carry over 8 to the next step.
- In the ten’s place, we add 27 + 81 + 8 (carried over) = 116. We put down 6 in the ten’s place and carry over 11 to the next step.
- In the hundred’s column, we have 9 + 45 + 11, this gives us 65. We put down 5 and carry over 6 to the next step.
- In the thousand’s place, we have3 + 9 + 6 = 18. We put down 8 and carry 1 to the next step.
- In the final step, we have 1 + 1 = 2.
- So our final answer is 28561.
Our sum on completion looks like this:
1 3 9 27 81
9 45 81
-----------------------
2 8 5 6 1
Answer:
(113)^4 = 28561.
2. Say we have to find (24)^4.
Here a is 2 and b is 4.
Step 1:
We raise a to the power of 4, which means (2)^4 = 16.
Step 2:
We then multiply the subsequent digits by 2 as b/a is 4/2 = 2. So our first line looks like this:
16 32 64 128 256
Step 3:
We will now do the next step for the second line.
- 32 gets multiplied by 3 to become 96.
- 64 gets multiplied by 5 to become 320.
- 128 gets multiplied by 3 to become 384.
Our sum looks like this now:
16 32 64 128 256
96 320 384
Step 4:
In our final step, we start adding from right to left. Remember, each column will give us a single digit.
- From 256 we put down 6 in the unit’s place and carry over 25 to the next step.
- In the ten’s place, we add 128 + 384 + 25 (carried over) = 537. We put down 7 in the ten’s place and carry over 53 to the next step.
- In the hundred’s column, we have 64 + 320 + 53, this gives us 437. We put down 7 and carry over 43 to the next step.
- In the thousand’s place, we have 32 + 96 + 43 = 171. We put down 1 and carry 17 to the next step.
- In the final step, we have 17 + 16 = 33.
- So our final answer is 331776.
Our sum on completion looks like this:
16 32 64 128 256
96 320 384
-----------------------------
33 1 7 7 6
Answer:
(24)^4 = 331776.
Solve the following example.
1. (14)^4
3. (25)^4
Ans : (14)^4 =38416.
2. (17)^4
Ans : (17)^4 = 83521.
Ans : (25)^4 = 390625.
The simplicity of this method can be vouched from examples given above.
You may try following examples.
1. (11)^4
2. (15)^4
3. (99)^4
4. (23)^4
5. (27)^4
In next blog we will discuss about "Raising to Fourth and Higher Powers-III".
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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