Roots and Radicals

Read the following SAT test question and then select the correct answer.

Read the question carefully to insure that you understand all of the information that you are given.  Then make a note of the bottom line so that you will be sure to solve for the correct information.  Assess your options for solving the problem and choose the most efficient method.  Attack the problem, solve it, and loop back to verify that your answer matches the bottom line.

If  , what is the value of ?

Bottom Line: You must find what  is equal to.

Assess your Options:  You could solve for x.  However, that is actually the long way to do this problem.  You are taking a timed test, so the long way is the wrong way!  Your bottom line is , so you can use what you know about radicals to solve the problem without solving for x.

Attack the Problem:  Look first at .  This is actually the same as  times 

.  Finding the square root of 4 is easy: .  Now you have .  Look back at the problem.  You are already given the square root of x!.  What is 2 times 16?  The answer is 32.  This is the process that you just followed:

Loop Back: Did you find the bottom line? Yes; .  Look down at your answer choices.

(A) 16
(B) 32
(C) 64
(D) 128
(E) 256

The correct answer is (B).


On sat.collegeboard.org, 36% of the responses were correct.

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