Math: 66bce0c1

ID: 66bce0c1

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

Comment: Remember that the square root symbol, √, represents the positive root only.

Method 1: Eyeballing the answers, the solution should come to you in about 5 seconds. Consider the equation with the root in isolation.

√(2x + 6) = x - 1

It is impossible for x to be negative or 0, since the root cannot yield a negative value. Hence, answer choices (A), (C), and (D) are all incorrect, meaning that (B) is the correct answer. Although it is not necessary, you can plug in 5 and quickly do the mental math, and yes, √16 = 4. Done and dusted.

Method 2: Although you could probably solve a little faster without a calculator, nothing is wrong with splitting the equation and entering the two halves independently into Desmos.

The intersection of the two functions occurs when x = 5, so the correct answer is (B). This might take a minute, but for a supposedly Hard question, that is still well above the pace necessary (i.e. faster than necessary) to finish the module in time.

Method 3: You can solve algebraically for practice.

√(2x + 6) = x - 1

2x + 6 = (x - 1)(x - 1)

2x + 6 = x^2 - 2x + 1

0 = x^2 - 4x - 5

0 = (x - 5)(x + 1)

x = 5 or -1

However, -1 is an invalid solution, since, as discussed above, in method 1, the right-hand side of the original equation cannot be -2. (C) is a good trap answer for the student who grinds out an answer without thinking to check whether it makes sense. Be careful with even-powered roots and absolute values, or squares (even exponents) for that matter. The correct answer is (B).