Math: 137cc6fd

ID: 137cc6fd

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: Substitution can reduce confusion, but knowing how to convert to exponential notation is a must.

Method 1: Let something like "m" represent 70n, since the actual term under the roots is irrelevant to the question (since it is the same throughout). Also, it is easier to work with exponential roots than with root symbols.

((m)^(1/5))((m)^(1/6))^2 = (m)^30x

(m^(1/5))(m^(2/6)) = m^30x

(m^(6/30))(m^(10/30)) = m^30x

m^(16/30) = m^30x

16/30 = 30x

16/900 = x

4/225 = x

The correct answer, in reduced form, is 4/225.

Method 2: You can type in the equation to Desmos, but I would recommend splitting it up and leaving out each 70, since, again, the number is incidental to the problem. Also, since Desmos graphs functions in terms of "x" and "y," you might want to swap places between "x" and "n." Finally, to input roots other than a square root, click on the "Show Keypad" button in the bottom-left corner, then the "functions" button, then scroll down in the menu all the way to the bottom. 

The closest the blue graph gets to the red one using the default range and step is when n = 0.1. Change the range to, say, 0 to 1 and the step to 0.01 for a higher degree of accuracy. Eventually, you will get the graphs to be closest when n = 0.018 with a step of 0.001, and 0.018 is acceptable as a rounded form of 4/225.

Given all of the back and forth outlined above, I would not recommend using this method to solve the question, but it is at least tenable if you have time to spare.

Method 3: A calculator can help make this problem much more manageable if it looks intimidating at first. Plug in a value greater than 1 for n, something like 2, and get to work.

Again, the closest value between the two functions is when n = 0.018. (0.017 takes the value of "y" all the way down to approximately 12.43.) Because the SAT requires only up to three digits to the right of the decimal, 0.018 must be a correct answer.