Eight Standard >> Cube and cube roots | Part -3

Q 1. Find the smallest number by which 686000 must be divided so that the quotient becomes a perfect cube number.

Solution:
  686000=686\(\times\)1000
        =\(2\times 7^{3} \times 10^{3}\)

So clearly if we devide this number by 2 we get a perfect cube.
Dividing 686000 \(\div\) 2
         =343000
         =\(7^{3} \times 10^{3}\)
         =\(70^{3}\) 

So the number is \(70^{3}\) 

Q 2. Find the smallest number by which 84375 must be multiplied so that product becomes a becomes a perfect cube.  

Solution:
  84375=\(3^{3}\times 5^{3} \times 5^{2}\)
    

So, clearly if we multipl 84375 by 5 we get a perfect cube.

So, the number is 5.