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Cube Roots

In this note I am going to tell you the world's fastest method to find the cube root of any \(6-digit number\). It takes nearly 2-3 mins to find the cube root but using this method you can find it in just 2 seconds.

For this trick you must know the cubes from numbers \(1 to 10\) and you will observe an interesting property.

\(1^3 = 1\) ---- Cubes ending in 1 have cube roots also ending in 1.

\(2^3 = 8\) ---- Cubes ending in 8 have cube roots ending in 2.

\(3^3 = 27\) ---- Cubes ending in 7 have cube roots ending in 3.

\(4^3 = 64\) ---- Cubes ending in 4 have cube roots ending in 4.

\(5^3 = 125\) ---- Cubes ending in 5 have cube roots ending in 5.

\(6^3 = 216\) ---- Cubes ending in 6 have cube roots ending in 6.

\(7^3 = 343\) ---- Cubes ending in 3 have cube roots ending in 7.

\(8^3 = 512\) ---- Cubes ending in 2 have cube roots ending in 8.

\(9^3 = 729\) ---- Cubes ending in 9 have cube roots ending in 9.

\(10^3 = 1000\) ---- Cubes ending in 0 have cube roots ending in 0.

Now you will observe an interesting property that cubes ending in 3 have cube roots ending in 7 and cubes ending in 7 have cube roots ending in 3. Another interesting property is that cubes ending in 2 have cube roots ending in 8 and cubes ending in 8 have cube roots ending in 2.

Now we will take an example:-

Find the cube root of 1728 = Which means the answer is ending in 2.

Now follow the next step to find the number in the tens place.

Make groups of 3 starting from units place = \( 1 , 728 , \)

The first group of 728 is done and the answer for that group is 2. Now take the next group which is 1. Find the smallest cube which you can subtract form 1. The smallest cube you can subtract is 1. So, the answer is \(12.\)

Note that I am not actually subtracting but I am just observing.

Lets take another example:-

Find the cube root of 614125.

= \( 614 , 125 , \) ---- { The answer is ending in 5 }

= The greatest cube you can subtract from 614 is 512 which is a cube root of 8.

So, the cube root of \(614125\) is \(85.\)

Note by Ashwin Korade
2 years, 7 months ago

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Well I know how to do the world's fastest method for 5th roots. BAM! :D Sharky Kesa · 2 years, 7 months ago

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@Sharky Kesa Tell us please @Sharky Kesa Krishna Ar · 2 years, 7 months ago

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@Krishna Ar Remember 1, 32, 243, 1024, 3125, 7776, 16807, 32768 and 59049. Notice that the units digit for each of these numbers are the units digit for their 5th roots. This is for all integer answers to the roots such that the integer is 1 or 2 digits. The rest you can follow from the note. Sharky Kesa · 2 years, 7 months ago

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Fantastic method bro.. Well said .... Akshay Sant · 2 years, 7 months ago

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Well said Mardokay Mosazghi · 2 years, 7 months ago

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