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Roots and Radicals

Algebra: Roots and Radicals

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

Always read the problem carefully and determine the bottom line, the question that you must answer.  Assess your options for solving the problem and choose the most efficient method to attack the problem.  When you have an answer, loop back to make sure that you completed all the necessary steps and solved for the bottom line.

If  , which of the following must be true?

Bottom Line: Which of the following . . . ?

Assess your Options:  Many "Which of the following . . . " questions require you to look at the answer choices to solve the problem, but you should always check to see whether you can simplify the equation that you have been given.  Instead of jumping to the answer choices, work the equation into a form that is not as intimidating.

Attack the Problem:  The original equation has a square root on each side.  How do you get rid of these square root signs?  Square both sides of the equation, and the roots will cancel out.  You are left with:

xa = x + b

You just showed that when something is on both sides of the equation, you can cancel it out.  There is a positive x on both sides of the equation.  If you subtract it from one side, you must subtract it from the other, and the x is eliminated.  You are left with:

-a = b

This looks fairly simple, so glance down at your answer choices.  All of them are set equal to 0.  Set your equation equal to zero by adding an a to each side.

0 = b + a

Remember, it doesn’t matter what order you use when adding two variables. 

Loop Back:  You put your answer in the same form as the answers on the test, so now all you have to do is match your answer to the correct one!

(A) a = 0
(B) b = 0
(C) a + b = 0
(D) a b = 0
(E) a² + b² = 0

The correct answer is (C).


On sat.collegeboard.org, 54% of the responses were correct.

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