Find out the Cube root of 19683

How to find out the value of cube root of 19683

 

We will find all the factors under the cube root of 19683 and then we will take three values at a time and when we apply the cube root on the complete prime factorization `then those three values which we have taken at a time then only one value out of three will come out. So let’s start – 

 

∛19683

 

Step 1:  There are 5 digits in the given number. So here we consider the first two digits from left, i.e.,  19and the last digit 3 from the unit place

 

Step 2: Our aim is to identify cube root of 19683. So, consider the two digit which of 19683. The first  two digit 19. Now, find the number having cube root as 19. If 19 is not cube root of any number take the smaller number than 19 that is 8 which is cube root of 2.

 

Step 3:  The nearest value of cube which is lesser than 19 is 8

2ᶟ= 8

 

Step 4: Now the first digit in the value of cube root of 19683 becomes 2

Let us assume the second digit after 2 be x (= 2x)

 

Step 5: To find the value of ‘x’ in 2x, which is the value of cube root of 19683.

According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 19683.

Now we know that the cube value of 7 is 343.

(for easy understanding, here 6 is the value of cube root of 343

i.e., when 7 multiplied thrice its value is 343. And in the value 19683 the last digit also is 7. Hence the unit digit is 7, x=7)

So the last digit in the unit place is 7

 

Step 6 : Hence the value of x in ∛19683 = 2x ,value of the last digit in unit place becomes 7

i.e., x= 7

Therefore, we can claim that the value of cube root of the given number 19683 is 27

 

Step 7:  The final answer can be expressed as ∛19683 = 27


Updated: October 21, 2021 — 11:35 am

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