A positive number added to its own square gives 552. Find the number.

The correct answer is Option (4) → 23

If the number is \(n\), then \(n+n^{2}=n(n+1)\), the product of two consecutive numbers. So 552 has to be split into two consecutive factors.

• \(n^{2}+n=552\), so \(n(n+1)=552\)

• \(552=23\times24\)

• The number is positive, so \(n=23\)

• Check: \(23+529=552\)

The number is 23.

Why the other options are incorrect

• Option (1) 24 — Incorrect. \(24+24^{2}=24+576=600\), not 552.

• Option (2) 22 — Incorrect. \(22+22^{2}=22+484=506\), not 552.

• Option (3) 26 — Incorrect. \(26+26^{2}=26+676=702\), not 552.