solve Z = A (1 + x) raised to 1/2 for the variable x

[maldous]

Hi

I have to solve for the letter x, heres the equation:

Z=A(1+x) raised to 1/2

how do i deal with the 1/2 exponent?

 

[royhaas]

It's the same as the square root.

 

[masters]

Here are two approaches to that problem:

Method 1: Retain rational exponent

\(\displaystyle Z=A(1+x)^\frac{1}{2}\)

Divide both sides by A.

\(\displaystyle \frac{Z}{A}=(1+x)^\frac{1}{2}\)

Square both sides.

\(\displaystyle \frac{Z^2}{A^2}=\left[\left(1+x\right)^\frac{1}{2}\right]^2\)

\(\displaystyle \frac{Z^2}{A^2}=1+x\)

Subtract 1 from both sides.

\(\displaystyle \frac{Z^2}{A^2}-1=x\)

\(\displaystyle x=\frac{Z^2-A^2}{A^2}\)

Method 2: Convert rational exponent to radical

\(\displaystyle Z=A(1+x)^\frac{1}{2}\)

\(\displaystyle Z=A \sqrt{1+x}\)

Divide both sides by A.

\(\displaystyle \frac{Z}{A}=\sqrt{1+x}\)

Square both sides.

\(\displaystyle \frac{Z^2}{A^2}=1+x\)

Complete as in Method 1......