How to find out the value of cube root of 21952
We will find all the factors under the cube root of 21952 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
∛21952
Step 1: There are 5 digits in the given number. So here we consider the first two digits from left, i.e., 21 and the last digit 2 from the unit place
Step 2: Our aim is to identify cube root of 21952. So, consider the two digit which of 21952. The first two digit 21. Now, find the number having cube root as 21. If 21 is not cube root of any number take the smaller number than 21 that is 8 which is cube root of 2.
Step 3: The nearest value of cube which is lesser than 21 is 8
2ᶟ= 8
Step 4: Now the first digit in the value of cube root of 21952 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 21952.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 21952.
Now we know that the cube value of 8 is 512.
(for easy understanding, here 8 is the value of cube root of 512
i.e., when 8 multiplied thrice its value is 512. And in the value 21952 the last digit also is 8. Hence the unit digit is 8, x=8)
So the last digit in the unit place is 8
Step 6 : Hence the value of x in ∛21952 = 2x ,value of the last digit in unit place becomes 8
i.e., x= 8
Therefore, we can claim that the value of cube root of the given number 21952 is 28
Step 7: The final answer can be expressed as ∛21952 = 28
Multiple choice Question
NO.1 ) What should be the One’s digit in the cube root for the cube number 21952?
a) 2
b) 3
c) 5
d) None
Answer is d) None
To find the value of ‘x’ in 2x, which is the value of cube root of 21952.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 21952.
Now we know that the cube value of 8 is 512.
(for easy understanding, here 8 is the value of cube root of 512
i.e., when multiplied thrice its value is 512. And in the value 21952 the last digit also is 8. Hence the unit digit is 8, x=8)
So the last digit in the unit place is 8
No.2) How many times 28 is multiplied to get the value 21952 ?
a) Two times
b) Three times
c) Four times
d) Five times
Answer is b) three times
Because 28 multiplied three times gives the value 21952 which means 28ᶟ= 21952