If the square root of a number is subtracted from the number, the result is 272. What is the number?
Show answer & explanation
Correct answer: A
Explanation
Let the number be x.
x − √x = 272
Let √x = y ⇒ x = y²
⇒ y² − y = 272
⇒ y² − y − 272 = 0
⇒ y² − 17y + 16y − 272 = 0
⇒ y(y − 17) + 16(y − 17) = 0
⇒ (y − 17)(y + 16) = 0
⇒ y = 17 (Positive value)
⇒ √x = 17
⇒ x = 17² = 289