Given $((9) \text{inches})^{1/2} = ((0.25) \text{yards})^{1/2}$, then which of the following statements is true?
- $((3) \text{inches}) = ((0.5) \text{yards})$
- $((9) \text{inches}) = ((1.5) \text{yards})$
- $((9) \text{inches}) = ((0.25) \text{yards})$
- $((81) \text{inches}) = ((0.0625) \text{yards})$
My question is : Can I apply here as $x^{1/2}=y^{1/2}$ then square both sides $\implies x=y$. But as given units are different. So,
Can you explain it, please?
Best Answer
If (one thing)$^\frac12$ = (another thing)$^\frac12$, then we can square both sides to get
Here, "one thing" is "$9$ inches", and "another thing" is "$0.25$ yards" (I don't know why you added all those parentheses!). Hence
Your worry about the units is irrelevant here, because they are inside the outer parentheses. This question is a reminder that $(9$ inches$)^\frac12$ is not the same as $9^\frac12$ inches.