# How to find the cube root of a number in less than 5 seconds?

Hi,

Cubes and cube roots are an essential part of many mathematical problems. Especially when you are preparing for a competitive exam its better equip yourself with all the tricks and shortcuts which cut short the time taken to solve the questions. Finding cube root can at times become tedious and lengthy enough if the given numbers are big. To help you save time in such situation we present here a technique with which you can find the cube root of any number in less than 5 seconds.

So let’s get started.

First things First!!

You need to remember the cubes of the first 10 natural numbers and some intersting patterns and relations which help us with our trick. Here you go,

Cube root                    Cube

1                   =     1

2                   =     8

3                   =     27

4                   =     64

5                   =    125

6                   =     216

7                   =     343

8                   =     512

9                   =     729

10                 =     1000

Observe the relation between the last digit(unit digit) of the cube root and the cube. Just take the number 27 for instance, the cube root is 3 i.e. So, if the last digit of the given number is 7 the last digit of the cube root will be 3. The reverse is also true. That is in the case of 343 the cube root is 7 thus understand and keep this relation between 7 and 3 in your mind.

You can observe and remember other numbers also like 2,8 (2^3 = 8 and 8^3 =512). For 1 its 1, for 0 its 0, 4 for 4, 5 for 5 and for 9 its 9.

Now, how to use this information in solving the problems.

Let’s try to solve one.

Q. Find the cube root of 4913.

Ans. Step1: Observe the last digit of the given number. Last digit = 3,                              thus as per our pattern analysis the last digit of the cube                               root is 7.

Step2: Next step is to discard the last three digits of the number                             4913. The number thus left out is digit 4.

Step3: Find out the nearest perfect cube less than 4, which is 1.                               Take the cube root of that number which is again 1. Thus                                our answer is 17.

Q. Find the cube root of 1092727.

Ans. Step1: Last digit is 7 therefore the last digit of the cube root is 3.

Step2: Striking out the last three digits 1092727. The left out                                    number is 1092.                                                                                                         Step3: The nearest perfect cube lesser than 1092 is 1000. Thus                                the remaining digits of the cube root are 10.                                                            Hence the cube root is 103.