Question

Given \({\left( {9{\rm{\;inches}}} \right)^{\frac{1}{2}}} = {\left( {0.25{\rm{\;yards}}} \right)^{\frac{1}{2}}}\).  Which one of the following statements is TRUE?
1. 3 inches = 0.5 yards
2. 9 inches = 1.5 yards
3. 9 inches = 0.25 yards
4. 81 inches = 0.0625 yards

Answer 1

Correct Answer - Option 3 : 9 inches = 0.25 yards

\({\left( {9{\rm{\;inches}}} \right)^{\frac{1}{2}}} = {\left( {0.25{\rm{\;yards}}} \right)^{\frac{1}{2}}}\)

Taking roots we have

\(3\sqrt {Inches} = 0.5\sqrt {Yards} \)

\(\frac{{\sqrt {inches} }}{{\sqrt {yards} }} = \frac{{0.5}}{3}\)

squaring both sides and cross multiplying we have 

9 inches = 0.25 yards

Method 2:

simply squaring both sides of the equation given in the question

we have 

9 inches = .25 yards