direktori wisata tirta 2012 (5)

8/12/2019 Direktori Wisata Tirta 2012 (5)

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Dhaval Bathia


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Dhaval Bathia

CUBE - ROOTS

The technique of solving cube-roots is one of the best

techniques of Vedic Maths. The cube-root of any perfectcube can be obtained in 2-3 seconds !

In every case, the answer can be obtained just by lookingat the question (and without any intermediate steps !)


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Dhaval Bathia

Number Cube

1 1

2 83 27

4 64

5 1256 216

7 343

8 512

9 729

10 1000

Even if you dont memorize the key itsall right.

Just go through the list a couple oftimes


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Dhaval Bathia

Number Cube

1 1

2 83 27

4 64

5 1256 216

7 343

8 512

9 729

10 1000

Have a look at the table given

here. You will notice that somenumbers are underlined

These underlined numbersestablish a unique relationshipamongst themselves:

It means :


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Dhaval Bathia

Number Cube

1 1

2 83 2 7

4 6 4

5 12 56 21 6

7 34 3

8 51 2

9 72 9

10 100 0

If cube ends in 1, cube root ends in 1

If cube ends in 8, cube root ends in 2If cube ends in 7, cube root ends in 3


If cube ends in 5, cube root ends in 5If cube ends in 6, cube root ends in 6






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Dhaval Bathia

Basically,

All Are Same Opposite Pairs

Last digit Last digit

Of Cube Of Cube Root

1 1

4 4

5 5

6 6

9 9

0 0

Last digit Last digit

Of Cube Of Cube Root

2 8

8 2

3 7

7 3


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Dhaval Bathia

Lets get to work straight away.

Three examples are given below

We will find the cube root in each case:

a) 2 6 2 1 4 4

b) 1 2 1 6 7

c) 1 1 7 6 4 9

Whenever a number is given to you, put a slash before the lastthree digits. It will help us in easily ascertaining the root. This will behow the numbers will look :


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Dhaval Bathia

Let us find the cube roots of each number:

2 6 2 1 4 4

We put a slash before the last three digits

The number ends in 4. We have seen that when the last digit of the cube is 4,the last digit of the cube root is also 4. So, our answer at this stage is __ 4.

Now we take the part to the left of the slash. The number to the left of theslash is 262.

Next, we have to find 2 perfect cubes between which the number 262 lies.From the key, it can be seen that 262 lies between 216 (the cube of 6) and343 (the cube of 7). Now, out of these 2 numbers 6 and 7we take thesmaller number and put it in the __ (dash).

Out of 6 and 7, the smaller number is 6. We take 6 and put it beside the 4obtained. Thus, the complete answer is 6 with 4.so 6 4.

The cube root of 262144 is 64.

1 2 3 4 5 6 7 8 9 10

1 8 27 64 125 216 343 512 729 1000


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Dhaval Bathia

Let us find the cube root of 12167:

1 2 1 6 7

We put a slash before the last three digits

The number ends in 7. We have seen that when the last digit of the cube is 7,the last digit of the cube root is also 3. So, our answer at this stage is __ 3.

Now we take the part to the left of the slash. The number to the left of theslash is 12.

12 lies between 8 (the cube of 2) and 27 (the cube of 3). Out of 2 and 3wetake the smaller number and put it in the __ (dash).

We take 2 and put it beside the 3 obtained. Thus, the complete answer is 2with 3.so 23.

The cube root of 12167 is 2 3.

1 2 3 4 5 6 7 8 9 10

1 8 27 64 125 216 343 512 729 1000


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Dhaval Bathia

Let us find the cube root of 117649:

1 1 7 6 4 9

The number ends in 9 so the cube root ends in 9. (Answer at this stage is _ 9)

117 lies between 64 and 125. So out of 4 and 5we take the smaller number4 and put it in besides 9.

The cube root of 117649 is 4 9.

1 2 3 4 5 6 7 8 9 10

1 8 27 64 125 216 343 512 729 1000


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Dhaval Bathia

1 2 3 4 5 6 7 8 9 10

1 8 27 64 125 216 343 512 729 1000

In the same manner, the cube-root of

2 8 7 4 9 6 = 6 6

1 7 5 6 1 6 = 5 6

9 7 0 2 9 9 = 9 9

1 0 3 8 2 3 = 4 7

After enough practice, you can get the answer just by looking at the numbers !


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Dhaval Bathia

In most school and college exams, cubes upto 6 digitsare asked. So what you have learnt till now is morethan enough. However, the same logic can be used indealing with bigger numbers

Let us take the example of a 7 digit number


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Dhaval Bathia

Suppose you are asked to find the cube-root of 1 4 0 4 9 2 8

1 2 3 4 5 6 7 8 9 10

1 8 27 64 125 216 343 512 729 1000

The number will be written as 1 4 0 4 9 2 8

The number ends in 8, so the root ends in 2. (Answer is ___ 2)

Now we come to the left part, 1404. Lets have a look at the key

The maximum number is 1000, so 1404 cannot be used in it. We will have toextend the number line

The cube of 11 is 1331 and the cube of 12 is 1728

1404 lies between these cubes (11 and 12) We take the smaller number 11 and put it beside the 2 already obtained.

The final answer is 11 2.

Thus, the cube root of 1404928 is 11 2

11 12

1331 1728

1404


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Dhaval Bathia

However, this extension of the number line is a rare phenomena. It is onlyexplained for academic purpose. Most numbers that we deal with are of 6 orless digits

Before terminating, it would be worthwhile to compare the normal method ofsolving cube roots with the Vedic method..

We all know, that in the normal method we use prime factors

We keep on dividing the cube till we get 1

Now for every 3 similar factors we take one factor and keep on multiplying

This technique is needlessly long, tiring and boring

The Vedic Math method helps us to get the answer instantly

Let us say we want to find the cube root of 262144,

We will do the comparison of the normal method and Vedic Method


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Dhaval Bathia

Question : Find the cube root of 262144 ?2 262144

2 131072

2 65536

2 32768

2 16384

2 8192

2 4096

2 2048

2 1024

2 512

2 256

2 128

2 642 32

2 16

2 8

2 4

2 2

NORMAL MATHS

2 x 2 x 2 x 2 x 2 x 2

= 64

Our Technique

262 144

= 6 4

Our Technique -- 2 steps !Normal Maths 20 steps


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Dhaval Bathia

Thus, we see that the Vedic Math Technique is much

more effective than the normal technique ofcalculating cube roots

direktori wisata tirta 2012 (5)

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