Roots and Radicals

Link of the Day

Every year 1.2 million students drop out. That's 857 students for every hour of every school day. In an effort to bring attention to this, College Board (the company that produces and administers the SAT) has set up 857 empty desks at the National Mall in Washington D.C. You can read more about College Board's "Don't Forget Ed" campaign here. This would make a great Excellent Example for your essay.

6/20 Algebra: Roots and Radicals

Read the following SAT question and then select your answer.

If square root (x minus a) = square root (x + b), which of the following must be true?

Step 1 of the Knowsys method for math is always to read the question carefully. Then, identify the bottom line. In this case, you need to select the answer choice that is true given the formula above. Step 3 is to evaluate your options. Think about what you could do, and what you should do. Since you have variables in the problem and in the answer choices, you could pick numbers for two of the variables, solve the equation for the third variable, and then look at the various answer choices. However, since this problem looks fairly straightforward, that's not necessary. It is faster and easier to simply manipulate and simplify the equation and then look at the answer choices (so this is what you should do). Note that if you did get stuck in the simplifying process, you could always go back and try the other method.

Start by squaring both sides of the equation.

Now, simply subtract x from both sides of the equation.

Lastly, add a to both sides of the equation.

Now, you know that a is equal to -b and you also know that the value of x doesn't matter (since it was eliminated). Take a look at the answer choices and see which one must be true. Don't forget to check answer choice (E) first and then work backwards. On "which of the following" questions, the test makers know that you will probably start with answer choice (A) and work your way down. Because they want you to as much time as possible, they usually put the correct answer near the end (not always, but usually).

Answer choice (E) would only be true if both a and b were equal to 0. Since you are looking for the answer choice that must be true, (E) won't work. You know that (D) is incorrect because it does not match the simplified form of the equation. (C) matches your prediction exactly. (B) and (A) both could be true, but they do not have to be true so neither of them is the correct answer choice.

The correct answer choice is (C).

On 57% of the responses were correct.

For more help with math, visit