Question

the product of 1372×a×b is a perfect cube where a×b is a perfect square. Then, the smallest possible value of (a+b) is​

Answer 1

1372 = 4× 343 = 4× 7³ = 2²×7³

for it to be perfect cube it should be multiplied with 2and 1

a=2, b=1

smallest value = 3

Answer 2

Answer: 8

Step-by-step explanation:

1. Prime factorization of 1372= 2 x 2 x 7 x 7 x 7

To make it a perfect cube, we can add another 2.

However, 2*1 is not a perfect square. So, we will add another 3 2s to make it a perfect cube.( 2x2x2x2x2x2x7x7x7)

Therefore, a*b= 2^4= 16

So, possibilities of a and b=

a=16                    a=4                  a=2

b=1                      b=4                  b=8

(sum) 17              (sum) 8            (sum) 10

Therefore, the smallest value of a+b = 8