How to find out the value of cube root of 4096
We will find all the factors under the cube root of 4096 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
∛4096
Step 1: There are 4 digits in the given number. So here we consider the first digit i.e.,4 and the last digit is 6
Step 2: Our aim is to identify cube root of 4096. So, consider the first digit which of 4096. The first digit 4. Now, find the number having cube root as 4. If 4 is not cube root of any number take the smaller number than 1 that is 1 which is cube root of 1.
Step 3: The nearest value of cube which is lesser than 4 is 1
1ᶟ= 1*1*1*= 1
Step 4: Now the first digit in the value of cube root of 3375 becomes 1
Let us assume the second digit after 1 be x (= 1x)
Step 5: To find the value of ‘x’ in 1x, which is the value of cube root of 4096.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 4096.
Now we know that the cube value of 6 is equal to 216.
(for easy understanding, here 6 is the value of cube root of 216
i.e., when 6 multiplied thrice its value is 216. And in the value 216 the last digit also is 6. Hence the unit digit is 6, x = 6 )
∛4096 = 16. So the last digit in the unit place is 16
Step 6: Hence the value of x in ∛4096 = 1x ,value of the last digit in unit place becomes 6
i.e., x = 6
Therefore, we can claim that the value of cube root of the given number 4096 is 16
Step 7: The final answer can be expressed as ∛4096 = 16
Hence the value of cube root of 4096 is 16.
Multiple choice Question
NO.1) What should be the value of unit’s digit in the cube root for the cube value 4096 ?
a) 8
b) 4
c) 6
d) None of the above
Answer is c) 6
We have to consider the last digit in the value 4096.
Now we know that the cube value of 6 is equal to 216.
(for easy understanding, here 6 is the value of cube root of 216
i.e., when 6 multiplied thrice its value is 216. And in the value 216 the last digit also is 6. Hence the unit digit is 6, x = 6 )
So the last digit in the unit place is 16
No.2) which of the following is the value of 16ᶟ ?
a) 4096
b) 4006
c) 4726
d) 4916
Answer is a)4096
Because 16 multiplied three times gives the value 4096 which means 16ᶟ= 4096