How To find out the value of cube root of 12167
We will find all the factors under the cube root of 12167 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 –
∛12167
Step 1: There are 5 digits in the given number. So here we consider the first two digits from left 12and the last digit 7
Step 2: Our aim is to identify cube root of 12167. So, consider the two digit which of 12167. The first two digit 12. Now, find the number having cube root as 12. If 12 is not cube root of any number take the smaller number than 12 that is 8 which is cube root of 2.
Step 3: The nearest value of cube which is lesser than 12 is 8
2ᶟ= 8
Step 4: Now the first digit in the value of cube root of 12167 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 12167.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 12167.
Now we know that the cube value of 3 is 27.
(for easy understanding, here 8 is the value of cube root of 27
i.e., when 3 multiplied thrice its value is 27. And in the value 12167 the last digit also is 7. Hence the unit digit is 3, x=3)
So the last digit in the unit place is 3
Step 6 : Hence the value of x in ∛12167 = 2x ,value of the last digit in unit place becomes 3
i.e., x = 3
Therefore, we can claim that the value of cube root of the given number 12167 is 23
Step 7: The final answer can be expressed as ∛12167 = 23
Multiple choice Question
NO.1 ) What should be the One’s digit in the cube root for the cube number 12167 ?
a) 2
b) 3
c) 8
d) 1
Answer is b) 3
According to the method to find the value of ‘x’ we have to consider the last digit of the value, 12167.
Now we know that the cube value of 3 is 27.
(for easy understanding, here 8 is the value of cube root of 27
i.e., when 3 multiplied thrice its value is 27. And in the value 12167 the last digit also is 7. Hence the unit digit is 3, x=3)
So the last digit in the unit place is 3
No.2) which of the following is the value of 23ᶟ ?
a) 12167
b) 40081
c) 68288
d) 59184
Answer is a) 12167
Because 23 multiplied three times gives the value 12167 which means 23ᶟ= 12167