**How to find out the value of cube root of 85184**

**We will find all the factors under the cube root of 85184 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., 85 and the last digit 4 from the unit place

__Step 2__: Now we have to find, if the value of a cube is 85. If there is no number found whose value of cube gives the value 85, then we have to consider the cube root number whose cube value is lesser than 85

__Step 3:__ The nearest value of cube which is lesser than 85 is 64

**4ᶟ= 64**

__Step 4__: Now the first digit in the value of cube root of 85184 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 85184.

According to the method to find the value of ‘x’ we have to consider the last digit of the cube value, 85184__.__

Now we know that the cube value of 4 is 64.

(for easy understanding, 4 is the value of cube root of64.

i.e., when __4 __multiplied thrice its value is 6__4__. And in the value 85184 the last digit also is 4. Hence the unit digit is 4, x=4)

So the last digit in the unit place is __4__

__Step 6 :__ Hence the value of x in **∛85184 ****= 44 ,value of the last digit in unit place becomes 4**

i.e., x= 4

Therefore, we can claim that the value of cube root of the given number 85184 is __44__

__Step 7: __The final answer can be expressed as ∛85184 = 44

**Multiple choice Question**

**NO.1) What should be the One’s digit in the cube root for the cube number 85184?**

a) 3

b) 4

c) 2

d) 8

**Answer is b) 4**

Now we know that the cube value of 4 is 64.

i.e., when 4 multiplied thrice its value is 6__4__. And in the value 85184 the last digit also is 4. Hence the unit digit is, x=4)

So the last digit in the unit place is __4__

**No.2) How many times 44 is multiplied to get the value 85184 ?**

a) Two times

b) Three times

c)Four times

d) Five times

**Answer is b) three times**

Because 44 multiplied three times gives the value 85184 which means 44ᶟ= 85184