A positive integer, when its positive square root is subtracted from it, gives 110. Find the positive integer.

Q.A positive integer, when its positive square root is subtracted from it, gives 110. Find the positive integer.

Let the positive square root of the number be \(x\). \(\therefore\) The number is \(x^2\) According to the question: \[ x^2 - x = 110 \Rightarrow x^2 - x - 110 = 0 \Rightarrow x^2 - (11 - 10)x - 110 = 0 \Rightarrow x^2 - 11x + 10x - 110 = 0 \Rightarrow x(x - 11) + 10(x - 11) = 0 \Rightarrow (x - 11)(x + 10) = 0 \] So, either \(x - 11 = 0\) i.e., \(x = 11\), or \(x + 10 = 0\) i.e., \(x = -10\) Since \(x\) is a positive square root, \(x \ne -10\) \(\therefore x = 11\) \(\therefore\) The number is \(x^2 = 11^2 = 121\) (Answer)