Question

Find the least number by which 31250 should be multiplied to make it a perfect cube and also find the cube root of the number obtained​

Answer 1

Step-by-step explanation:

31250 = 5 x 5 x 5 x 5 x 5 x 5 x 2         (prime factorization)

31250 x 2 x 2 = 5 x 5 x 5 x 5 x 5 x 5 x 2 x 2 x 2 (multiplying 2 x 2 in lhs and rhs)    

31250 x 4 = 5 x 5 x 5 x 5 x 5 x 5 x 2 x 2 x 2

therefore 4 is the smallest number to be multiplied by 32150 to make a perfect cube

125000 = 5 x 5 x 5 x 5 x 5 x 5 x 2 x 2 x 2

∛125000 = ∛ 5³ x 5³ x 2³

∛125000 = 5 x 5 x 2

∛125000 = 50

hope this helps you.