MATHS TRICKS: CUBE ROOT

Cube Root of a given perfect given in any exam can be found out quickly, easily and effortlessly. This article shows you how. Before going to the method you should keep in mind the following…

While preparing for exam, write down cubes of 1 to 10 and learn it by heart.

1 x1x1 =1

2x2x2=8

3x3x3=27

4x4x4=64

5x5x5=125

6x6x6=216

7x7x7=343

8x8x8=512

9x9x9=729

10x10x10=1000

Now if you observe the above cubes closely, you will find that the unit places of any perfect cube can be only any of these….

1 or 8 or 7 or 4 or 5 or 6 or 3 or 2 or 9 or 0

This information is very important.

How will it help you? Let us learn through an example..

Suppose you got a number = 12167

You have to find the cube root of 12167.

Now you should quickly make out that since unit place of 12167 = 7, the unit place of the cube root of 12167 should be = 3 .

If the given number is 328509 then you should immediately tell to yourself that since unit place of 328509 is 9, the unit place of cube root of 328509 should be = 9

RULE 1

In the same way learn the following by heart .. On the left side is the unit digit of perfect cube and on the right side unit digit of cube root

If cube has unit digit as 1 = cube root has unit digit as 1

8 = 2

7 = 3

4 = 4

5 = 5

6 = 6

3 = 7

2 = 8

9 = 9

RULE 2

If the given perfect cube has 4 or 5 or 6 digits then the cube root will have = 2 digits

Eg: cube root of 12167 = 23,

cube root of 704969= 89

If the given perfect cube has 7 or 8 or 9 digits then cube root will have = 3 digits

IMPORTANT TIP: Try to group the numbers in a set of 3 digits from Right to left and the number of such groups you get is the number of digits in your cube root

Eg: 12167 can be grouped as 12 and167 ( RIGHT TO LEFT …SET OF THREE DIGITS)

Therefore the number of digits in cube root should be 2 as there are only two such groups….

Eg 704969 can be grouped as 704 and 969

Therfore the number of digits in cube root should be 2

LET US LEARN NOW HOW TO FIND OUT CUBE ROOTS OF A GIVEN PERFECT  CUBE QUICKLY

Q)  The cube root of 21952 is ?

a) 18 b) 19 c) 28 d) 148

Ans) Let us learn the trick step by step

STEP 1 : The cube has unit digit =2 ,   therefore the cube root should have unit digit = 8

So you can eliminate the option b

STEP 2: The number 21952 can be grouped as 21 and 952  (Right to left in batches of three digits)

So your cube root should have two digits. Now you can eliminated option d

STEP 3: VERY IMPORTANT………….

21952 =

We know 20 cube = 8000 and 30 cube = 27000

So our cube root lies between these two that is 20 or 30

As we know that the unit digit should be 8 , the answer is 28

Q) Find out the cube root of 250047 ?

Ans) STEP 1 : The unit digit of cube = 7 therefore unit digit of cube root = 3

STEP 2 : Group the cube…into 250 and 047. So the cube root has 2 digits

STEP 3.Finally, we know that 60 cube = 216000 and 70 cube= 343000

250047 lies between 216000 and 343000

Therfore the cuberoot should lie between 60 and 70

We know that unit number should be 3

Therefore the number is 63