Question

Find the value of 2a+3b if a and b are positive integers and a^2b^3=108

Answer 1

4 + 9 = 13

Explanation:

Start by prime factorizing 108. 108 is equal to
`2^2 \cdot 3^3`. This conveniently makes the a and b we need, as we are looking for
`a^2 \cdot b^3`. We get
`a=2,b=3`. Now, plug this into
`2a+ 3b`. We get
`2 \cdot 2 + 3 \cdot 3 = 4 + 9 = 13`.