How to calculate N-th root using calculator with [SQRT] key

Mr.Calculator

[Japanese]

Do you know we can calculate 3rd root, 5th root using standard calculator with Square Root key [SQRT]? Following is the method how to do it

This is the calculator of the Mr.Calculator abacus.

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As shown above, Memory Clear is assigned to [CM] key and Memory Read (Recall) key is assigned to [RM] key. In this article we use [MC] and [MR] respectively as used by the standard calculator.

Some calculator has [MRC] key instead of [MC] and [MR] key. If you press [MRC] key once, it means [MR] and If you press [MRC] key twice, it means [MC].

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For example, 4th root is calculated by Square root twice and 6th root is calculated by multiplication of square root and cube root. It is enough to know the calculation method of N-th root where N is prime number greater than 2.


3rd root of A (Cube root of A)

[MC] A [M+] [SQRT] [SQRT]
[x] [MR] [=] [SQRT] [SQRT]
[x] [MR] [=] [SQRT] [SQRT]
Repeat until convergence.

5th root of A

[MC] A [M+] [SQRT] 3 times
[x] [=] [=] [x] [MR] [=] [SQRT] 3 times
[x] [=] [=] [x] [MR] [=] [SQRT] 3 times
Repeat until convergence.

7th root of A

[MC] A [M+] [SQRT] 3 times
[x] [MR] [=] [SQRT] 3 times
[x] [MR] [=] [SQRT] 3 times
Repeat until convergence.

11th root of A

[MC] A [M+] [SQRT] 4 times
[x] [=] 4 times [x] [MR] [=] [SQRT] 4 times
[x] [=] 4 times [x] [MR] [=] [SQRT] 4 times
Repeat until convergence.

13th root of A

[MC] A [M+] [SQRT] 4 times
[x] [=] [=] [x] [MR] [=] [SQRT] 4 times
[x] [=] [=] [x] [MR] [=] [SQRT] 4 times
Repeat until convergence.


Let's confirm the methods with actual value. I show you only value transition and the value calculated with iPhone's scientific calculator.


3rd root of 10

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5th root of 10

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7th root of 10

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11th root of 10

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13th root of 10

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As a matter of fact, we can calculate N-th root using calculator WITHOUT [SQRT] key. I'll show you the method in the next article.


Related articles:

How to solve Cube root of 1729.03 using abacus? (Feynman v.s. Abacus man)
http://blog.goo.ne.jp/ktonegaw/e/cff5d6e7ecaa07230b9cc7af10b23aed

Index: Square root and Cube root using Abacus
http://blog.goo.ne.jp/ktonegaw/e/f62fb31b6a3a0417ec5d33591249451b


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