Question

Find the smallest number by which each
of the following numbers must be
multiplied to obtain a perfect cube.
a. 1296

​

Answer 1

Answer:

36

Step-by-step explanation:

Let us first split the number 1296 in its prime factors

So,

1296=2×2×2×2×3×3×3×3

So,

For this number to be a perfect cube the prime factors must be of the number which is divisible by 3

So we can see that there are four 3s and four 2s in the number 1296 prime factors

So, to make this perfect cube, there should be more two 3s and two 2s in the multiplications of the new formed number(Six 3s and Six 2s)

This is because 6 is the least number greater than 4 which is divisible by 3

So,

New number= 2×2×2×2×2×2×3×3×3×3×3×3

                    =46656 (Which is a perfect cube)

So, the least number that can be multiplied to make 1296 a perfect cube is  

2 ×2×3×3

=36

So, 36 is the required number