How to find out the value of cube root of 8000
We will find all the factors under the cube root of 8000 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 –
∛8000
Step 1: There are 4 digits in the given number. So here we consider the first digit i.e.,8 and the last digit is 0
Step 2: Our aim is to identify cube root of 8000. So, consider the first digit which of 8000. The first digit 8. Now, find the number having cube root as 8 The value of cube of 2 is 8.
Step 3: We know that The value of cube of 2 is 8.
2ᶟ = 2*2*2*= 8
Step 4: Now the first digit in the value of cube root of 8000 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 8000.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 8000.
Now we know that the cube value of 10 is1000.
(for easy understanding, here 10 is the value of cube root of 1000
i.e., when 10 multiplied thrice its value is 1000. And in the value 8000 the last digit also is 0. Hence the unit digit is 0. i.e. x = 0
So the last digit in the unit place is 0
Step 6 : Hence the value of x in ∛8000 = 2x ,value of the last digit in unit place becomes 0
i.e., x = 0
Therefore, we can claim that the value of cube root of the given number 8000 is 20
Step 7: The final answer can be expressed as ∛8000 = 20
Hence the value of cube root of 8000 is 20.
Multiple choice Question
NO.1) how to find out the unit’s digit in the cube root for the cube value 8000?
a) By squaring the last digit of the value
b) By finding the value of cube root whose last digit of the value ends with 0
c) The last digit is 0, hence the unit digit in cube root value is also 0
d) By prime factorization
Answer is b)
We have to consider the last digit in the value 8000.
Now we know that the cube value of 10 is 1000.
(for easy understanding, here 10 is the value of cube root of 1000
i.e., when 10 multiplied thrice its value is 1000. And in the value 8000 the last digit also is 0. Hence the unit digit is , x = 0)
No.2) which of the following is the value of 20ᶟ ?
a) 8000
b) 4000
c) 6828
d) none
Answer is a) 8000
Because 20 multiplied three times gives the value 8000.