Carcass wrote:
Quantity A |
Quantity B |
\(\frac{\sqrt{25}}{\sqrt{10}}\frac{\sqrt{8}}{\sqrt{15}}\) |
\(\frac{\sqrt{51}}{\sqrt{46}}\frac{\sqrt{23}}{\sqrt{34}}\) |
There are so many ways to do this problem!
The first is the most certain : Use the calculator. It has a √ button, so you can actually use it to compare these values if you carefully work through the proper order of operations. If you have difficulty with exponents and radicals spend the 1-2 minutes on the certain, methodical approach.
However, there is also a relatively simple method for logically estimating the relationship based on the idea that if all values in a system of multiplication or division have the same radical or exponent you can combine the terms through multiplication or division while keeping the exponent or radical.
So, let's look at that logical estimation method. First, eliminate Choice D, because there are no variables so the relationship must be definitive.
Now, let's look at Quantity A and imagine that the radicals are gone, so we'd simply be looking at (25/10) x (8/15).
Estimate roughly to convert that into Quantity A is 2.5 x .5 ≈ 1.25.
Sure, there is a √ but we can basically ignore it because it's in Quantity B as well.
Next, let's look at Quantity B and imagine that the radicals are gone, so we'd simply be looking at (51/46) x (23/34).
Estimate roughly to convert that into Quantity A is 1.1 x .667 ≈ .75.
Once again ignoring the √ we can easily see that roughly .75 < roughly 1.25 so Quantity A is greater and we can select Choice A.