Calculation Of Cube Root Of Perfect Cubes Up To 1 Million In Seconds!

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Finding cube roots of numbers could be really time taking by using conventional methods. Here is a trick to calculate cube roots of perfect cube numbers having values as large as 1 million in a matter of seconds.

Prerequisite:

You need to know cube of first 10 natural numbers to implement this trick. See the table 1 below.

table 1: cubes of first 10 natural numbers

OBSERVATION:

Here we can make an observation ,see the table 2 below:

table 2

Here the observation is that numbers ending with 1,4,5,6,9,0 have their cube roots ending with the same last digit(1,4,5,6,9,0 respectively)while (2,8) and (3,7) have number and cube roots ending with each other.

Method:

STEP 1: separate the last 3 digits of the number given. Example:

103|823

STEP 2: see the last digit of the last 3 digit number. In this example we have 3 as last digit.

STEP 3: now see the second table , find the last digit of the cube root of the number ending with the number obtained in step 2. Here number ending with 3 has it’s cube root ending with 7.

ANSWER: _____7

STEP 4: Now see the leftover digits.

103|823

in this example we have 103 as leftover number. Now find the number 103 lies between 64(cube of 4) and 125(cube of 5). We would take the smaller number out of the two; here 4 would be the number.

ANSWER: 47

STEP 5: You have obtained the answer!!! Congratulations!!!👏

Example:

find cube root of 39304

39304

39|304

4->4

Answer: ___4

39

27 (3x3x3) <39<64 (4x4x4)

so we choose 3 ; as 3 is the greatest number with its’s cube≤39.

Answer: 34

So now you are a math's wizard!!!🧙‍♂ ️Go and show off the cool stuff you have just learnt!