Next Perfect Square

If x is a perfect square (i.e., the square of some integer), then the next perfect square larger than x is:

  1. x + 1
  2. x2 + 1
  3. x2 + 2x + 1
  4. x2 + x
  5. x + 2√x + 1


Show/Hide Solution

Let x = n2. Then √x = n. The next perfect square after x will be the square of n + 1. So we want (n + 1)2 in terms of x.

(n + 1)2 = n2 + 2n + 1 = x + 2√x + 1. The answer is (e).

Check: Let x = 49; then n = 7. So n + 1 = 8, and (n + 1)2 = 64.

Is 64 the next perfect square after 49? Yes.

Does x + 2√x + 1 = 64? Yes, 49 + 2 · 7 + 1 = 49 + 14 + 1 = 64.

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