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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10, AMC-12.

Which of the following expressions is a perfect square?

Expressions with radicals are tricky:

equation

equation

equation

We see that all the expressions above are perfect squares.

The expression:

equation

and since no two perfect squares can differ by 1, it cannot be a perfect square no matter how we try to rearrange the terms.