How To find out the value of cube root of 32768
We will find all the factors under the cube root of 32768 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 –
Step 1: There are 5 digits in the given number. So here we consider the first two digits from left, i.e., 32 and the last digit 8 from the unit place
Step 2: Now we have to find, if the value of a cube is 32. If there is no number found whose value of cube gives the value 8, then we have to consider the cube root number whose cube value is lesser than 32
Step 3: The nearest value of cube which is lesser than 32 is 27
3ᶟ= 27
Step 4: Now the first digit in the value of cube root of 32768 becomes 3
Let us assume the second digit after 3 be x (= 3x)
Step 5: To find the value of ‘x’ in 3x, which is the value of cube root of 32768.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 32768.
Now we know that the cube value of 8 is 2.
(for easy understanding, 2 is the value of cube root of 8
i.e., when 2 multiplied thrice its value is 8. And in the value 32768 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 ∛32768 = 32 ,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 32768 is 32
Step 7: The final answer can be expressed as ∛32768 = 32
Multiple choice Question
NO.1 ) What should be the One’s digit in the cube root for the cube number 32768?
a) 2
b) 3
c) 5
d) None
Answer is a) 2
To find the value of ‘x’ in 3x, which is the value of cube root of 32768.
According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 32768.
Now we know that the cube value of 2 is 8.
(for easy understanding, here 2 is the value of cube root of 8
i.e., when multiplied thrice its value is 8. And in the value 32768 the last digit also is 2. Hence the unit digit is 2, x=2)
So the last digit in the unit place is 2
No.2) How many times 32 is multiplied to get the value 32768 ?
a) Two times
b) Three times
c) Four times
d) Five times
Answer is b) three times
Because 32 multiplied three times gives the value 32768 which means 32ᶟ= 32768