M maldous New member Joined Jun 22, 2008 Messages 1 Jun 22, 2008 #1 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?
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?
R royhaas Full Member Joined Dec 14, 2005 Messages 832 Jun 22, 2008 #2 It's the same as the square root.
M masters Full Member Joined Mar 30, 2007 Messages 378 Jun 22, 2008 #3 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......
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......
