Question

if a positive number exceeds its positive square roots by 12,then find the number.

Answer 1

Let the number is x.
According to the question,
x - √x =12
⇒ x - 12 = √x
⇒ (x-12)² = (√x)²
⇒ x²+144-24x = x
⇒ x² -25 x+144=0
⇒ x² -16 x-9x+144=0
⇒ x(x-16)-9(x-16) = 0
⇒ (x-16)(x-9) = 0
⇒ x = 16 or 9

when x = 16, √x = 4; x-√x = 12 (satisfied)
when x = 9, √x = 3; x-√x = 6 (not satisfied)

So the number is 16.

Answer 2

Let the number be x
Its square root be √x
x - √x = 12
x - 12 = √x
squaring on both sides
x²-24x+144 = x
x² - 25x + 144 = 0

(x-16)(x-9) = 0

x = 16 or 9