Carcass wrote:
If a and b are positive and \(\frac{ab}{x}=\sqrt{a}\) then \(\frac{x}{b^2}=\)
A. \(\sqrt{a}\)
B. \(\frac{\sqrt{a}}{b}\)
C. \(\frac{a}{b^2}\)
D. \(\sqrt{ab}\)
E. \(\sqrt{\frac{a}{b}}\)
Kudos for the right answer and explanation
Rather than attempt a lot of algebraic manipulations, we can simply find values of a, b and x that satisfy the given equation and then test the answer choices...
If \(\frac{ab}{x}=\sqrt{a}\), then it COULD be the case that a = 4, b = 3 and x = 6, since these values satisfy the given equation.
The question asked us to find the value of \(\frac{x}{b^2}\)
So, plug a = 4, b = 3 and x = 6 into the expression to get: \(\frac{x}{b^2}=\frac{6}{3^2}=\frac{6}{9}=\frac{2}{3}\)
So, when a = 4, b = 3 and x = 6, \(\frac{x}{b^2}=\frac{2}{3}\)
This means the correct answer will be the one that evaluates to equal 2/3 when we plug in a = 4, b = 3 and x = 6....
A. \(\sqrt{4}\) = 2. NO GOOD. We want the expression to evaluate to be 2/3
B. \(\frac{\sqrt{4}}{3}\) = 2/3.
Perfect! C. \(\frac{4}{3^2}\) = 4/9. NO GOOD. We want the expression to evaluate to be 2/3
D. \(\sqrt{(4)(3)}\) = √12. NO GOOD. We want the expression to evaluate to be 2/3
E. \(\sqrt{\frac{4}{3}}\) = 2/√3. NO GOOD. We want the expression to evaluate to be 2/3
Answer: B
Cheers,
Brent