Baumol Model – June 2015 Exam

Good Evening sir,

Regarding Section A Question #15 of the 2015 June Exam the questions goes like this: A company needs $150,000 each year for regular payments. Converting the company’s short term investments into cash to meet these regular payment incurs a Fixed Cost of $400 per transaction. These short term investments pay interest of 5% per year while the company earns interest of only 1% per year on cash deposits.

What is the Optimum amount of short term investment to convert into cash in each transaction using Baumol Model?

And the answer is:

(2 x 400 x 150,00/(0.05-0.01))^0.5

Everything is clear to me except the exponent 0.5 at the end. What is the reason behind that?

Thanks for the help, sir