How to find out the value of cube root of 10648
We will find all the factors under the cube root of 10648 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 –
∛10648
Step 1: There are 5 digits in the given number. So here we consider the first two digits from left 10 and the last digit 8
Step 2: Our aim is to identify cube root of 10648. So, consider the two digit which of 10648. The first twodigit 10. Now, find the number having cube root as 10. If 10 is not cube root of any number take the smaller number than 10 that is 8 which is cube root of 2.
Step 3: The nearest value of cube which is lesser than 10 is 8
2ᶟ= 8
Step 4: Now the first digit in the value of cube root of 10648 becomes 2
Let us assume the second digit after 1 be x (= 2x)
Step 5: To find the value of ‘x’ in 2x, which is the value of cube root of 10648.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 10648.
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 10648 the last digit also is 2. Hence the unit digit is 2, x = 2)
So the last digit in the unit place is 2
Step 6 : Hence the value of x in ∛10648 = 2x ,value of the last digit in unit place becomes 2
i.e., x= 2
Therefore, we can claim that the value of cube root of the given number 10648 is 22
Step 7: The final answer can be expressed as ∛10648 = 22
Multiple choice Question –
NO.1) For 5-digit value, How many digits of cube value is considered leaving the last unit place?
a) 2 digits from the left
b) 1 digit from the left
c) 1 digit from the right
d) 3 digits from the left
Answer is a)
We considered the first two digits in the value 10648.
No.2) which of the following is the value of 22ᶟ?
a) 10648
b) 4008
c) 6828
d) 5918
Answer is a) 10648
Because 22 multiplied three times gives the value 10648 which means 22ᶟ= 10648