Free Digital SAT Math Radical and Exponential Expressions Quiz

Radical and Exponential Expressions

Question 1 of 5

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A student solved the equation \(\sqrt{x+11}=x-1\) by squaring both sides and obtained the two values \(x=5\) and \(x=-2\). The graphs of \(y=\sqrt{x+11}\) and \(y=x-1\) are shown below.

Which of the following statements about the solutions of \(\sqrt{x+11}=x-1\) is correct?

Select one option.

Both \(x=5\) and \(x=-2\) are solutions.
Only \(x=5\) is a solution; \(x=-2\) is extraneous because \(x-1\) is negative when \(x=-2\), but \(\sqrt{x+11}\) is never negative.
Only \(x=-2\) is a solution; \(x=5\) is extraneous.
Neither value is a solution, so the equation has no real solutions.
Only \(x=5\) is a solution; \(x=-2\) is extraneous because \(x+11\) is negative when \(x=-2\).

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