Shortcut to Find Cube Root of a Number by Top Competitive Institute for Banking, SSC, Railway

1. REMEMBERING UNITS DIGITS

First we need to remember cubes of 1 to 10 and unit digits of these cubes. The figure below shows the unit digits of cubes (on the right) of numbers from 1 to 10 (on the left).

Now look at the image above. We can definitely say that:

Whenever unit digit of a number is 9, the unit digit of the cube of that number will also be 9. Similarly, if the unit digit of a number is 9, the unit digit of the cube root of that number will also be 9. Similarly, if unit digit of a number is 2, unit digit of the cube of that number will be 8 and vice versa if unit digit of a number is 8, unit digit of the cube root of that number will be 2. Similarly, it will be applied to unit digits of other numbers as well.

2. DERIVING CUBE ROOT FROM REMAINING DIGITS

Let’s see this with the help of an example. Note that this method works only if the number given is a perfect cube.

Q. Find the cube root of 474552.

Unit digit of 474552 is 2. So we can say that unit digit of its cube root will be 8.

Now we find cube root of 447552 by deriving from remaining digits.

Let us consider the remaining digits leaving the last 3 digits. i.e. 474.

Since 474 comes in between cubes of 7 and 8.

So the ten’s digit of the cube root will definitely be 7

i.e. cube root of 474552 will be 78.

Let us take another example.

Q. Find the cube root of 250047.

Since the unit digit of the number is 7, so unit digit in the cube root will be 3.

Now we will consider 250.

Since, 6³ < 250 < 7³, So tens digit will be 6

So we find cube root of the number to be 63.

Here are some more examples.

Q. Simplify: ∛970299 = ?

Unit digit of number is 9

∴ Unit digit of cube root will be 9

Now we will consider 970

Since, 9³ < 970 < 10³

So, we find cube root of the number to be 99.
Let’s take another example to make this trick clearer to you.

Q. Simplify: ∛140608 = ?

Unit digit of number is 8

∴ Unit digit of cube root will be 2

Now we will consider 140

Since, 5³ < 140 < 6³

So, we find cube root of the number to be 52.

This trick in only helpful for finding out cube root of a perfect cube.

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