How To find out the value of cube root of 6859
We will find all the factors under the cube root of 6859 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 –
∛6859
Step 1: There are 4 digits in the given number. So here we consider the first digit i.e.,6 and the last digit is 9
Step 2: Our aim is to identify cube root of 6859. So, consider the first digit which of 6859. The first digit 6. Now, find the number having cube root as 6. If 6 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 6 is 1
1ᶟ= 1*1*1*= 1
Step 4: Now the first digit in the value of cube root of 6859 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 6859.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 6859.
Now we know that the cube value of 9 is729.
(for easy understanding, here 9 is the value of cube root of 729
i.e., when 9 multiplied thrice its value is 729. And in the value 6859 the last digit also is 9. Hence the unit digit is 9 x=9 )
∛6859= 19. So the last digit in the unit place is 9
Step 6 : Hence the value of x in ∛6859 = 19 ,value of the last digit in unit place becomes 9
i.e., x= 9
Therefore, we can claim that the value of cube root of the given number 6859 is 19
Step 7: The final answer can be expressed as ∛6859 = 19
Hence the value of cube root of 6859 is 19.
Multiple choice Question
NO.1) how to find out the unit’s digit in the cube root for the cube value 6859 ?
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 9
c) The last digit is 9, hence the unit digit in cube root value is also 9
d) By prime factorization
Answer is b) By finding the value of cube root whose last digit of the value ends with 9
We have to consider the last digit in the value 6859.
Now we know that the cube value of 9 is 729.
(for easy understanding, here 8 is the value of cube root of 729
i.e., when 9 multiplied thrice its value is 729. And in the value 6859 the last digit also is 2. Hence the unit digit is , x=9)
No.2) which of the following is the value of 18ᶟ?
a) 6858
b) 4008
c) 6828
d) none
Answer is d) None
Because 18 multiplied three times gives the value 6859.