Quick question on a simplification of position formula

[skurred]

Homework Statement

I'm having issues simplifying the following position formula.

Homework Equations

http://imgur.com/y1tgG.jpg

The Attempt at a Solution

Its probably something really stupid I'm not realizing but i don't understand how under the square root 127 got to be 127 and not 127^2.

Since in the orig problem when you solve for V^2 you'd end up with

V^2= (127^2)(g)/ ((2)(80.8))
[

 

[tiny-tim]

Welcome to PF!

Hi skurred! Welcome to PF!

(try using the X² tag just above the Reply box )

Yes, you're right … (g/2)(127/v)² = 80.8, so v = 127√(g/(2*80.8))

(is this from a book? )

 

[Architeuthis Dux]

This is a simplification of the position formula.]

Hi there,

It's actually not a stupid question at all! The reason why 127^2 becomes 127 under the square root is because of the power rule for exponents. When taking the square root of a number raised to a power, you can simply divide the power by 2. In this case, 127^2 becomes 127^(2/2) which simplifies to 127^1, or just 127.

So in the original problem, when solving for V^2, you would end up with (127^2)(g)/((2)(80.8)) which simplifies to (127^(2/2))(g)/((2)(80.8)), which then becomes 127(g)/((2)(80.8)) or just 127(g)/161.6.

I hope this helps! Let me know if you have any other questions.