How To find out the value of cube root of 103823
We will find all the factors under the cube root of 103823 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 –
∛103823
Step 1: There are 6 digits in the given number. So here we consider the first three digits from left, i.e., 103 and the last digit 3 from the unit place
Step 2: Our aim is to identify cube root of 103823. So, consider the first three digits which of 103823. The first three digits are 103. Now, find the number having cube root as 103. If 103 is not cube root of any number take the smaller number than 103 that is 64 which is cube root of 4
Step 3: The nearest value of cube which is lesser than 103 is 64
4ᶟ= 64
Step 4: Now the first digit in the value of cube root of 103823 becomes 4
Let us assume the second digit after 4 be x (= 4x)
Step 5: To find the value of ‘x’ in 4x, which is the value of cube root of 103823.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 103823.
Now we know that the cube value of 7 is 343.
(for easy understanding, 7 is the value of cube root of 343.
i.e., when 7 multiplied thrice its value is 343. And in the value 103823 the last digit also is 3. 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 ∛103823 = 47 ,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 103823 is 47
Step 7 : The final answer can be expressed as ∛103823 = 47
Multiple choice Question
NO.1) What should be the One’s digit in the cube root for the cube number 103823 ?
a) 3
b) 4
c) 2
d) 7
Answer is d) 7
Now we know that the cube value of 7 is 343.
i.e., when 7 multiplied thrice its value is 343. And in the value 103823 the last digit also is 3. Hence the unit digit is, x=7)
So the last digit in the unit place is 7
Q.No.2) How many times 47 is multiplied to get the value 103823?
a) Two times
b) Three times
c) Four times
d) Five times
Answer is b) three times
Because 47 multiplied three times gives the value 103823 which means 47ᶟ= 103823