How to find out the value of cube root of 13824
We will find all the factors under the cube root of 13824 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 –
Step 1: There are 5 digits in the given number. So here we consider the first two digits from left 13and the last digit 4
Step 2: Our aim is to identify cube root of 13824. So, consider the two digit which of 13824. The first two digit 13. Now, find the number having cube root as 13. If 13 is not cube root of any number take the smaller number than 13 that is 8 which is cube root of 2.
Step 3: The nearest value of cube which is lesser than 13 is 8
2ᶟ= 8
Step 4: Now the first digit in the value of cube root of 13824 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 13824.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 13824.
Now we know that the cube value of 4 is 64.
(for easy understanding, here 4 is the value of cube root of 64
i.e., when 4 multiplied thrice its value is 64. And in the value 13824 the last digit also is 4. Hence the unit digit is 4, x=4)
So the last digit in the unit place is 4
Step 6 : Hence the value of x in ∛13824 = 24 ,value of the last digit in unit place becomes 4
i.e., x= 4
Therefore, we can claim that the value of cube root of the given number 13824 is 24
Step 7: The final answer can be expressed as ∛13824 = 24
Multiple choice Question
NO.1 ) What should be the One’s digit in the cube root for the cube number 13824?
a) 2
b) 3
c) 8
d) None
Answer is d) none
According to the method to find the value of ‘x’ we have to consider the last digit of the value, 13824.
Now we know that the cube value of 4 is 64.
(for easy understanding, here 8 is the value of cube root of 64
i.e., when 4 multiplied thrice its value is 64. And in the value 13824 the last digit also is 64. Hence the unit digit is 4, x=4)
So the last digit in the unit place is 4
No.2) How many times 24 is multiplied to get the value 13824?
a) Two times
b) Three times
c) Four times
d) Five times
Answer is b) three times
Because 24 multiplied three times gives the value 13824 which means 24ᶟ= 13824