Question

If the sum of a number and its positive square root is 6/25,then find the number.

Answer 1

Let the number be x.
Given,
$x + \sqrt{x} = \frac{6}{25} \\ 25x + 25 \sqrt{x} = 6 \\ 25x - 6 =25 \sqrt{x} \\ {(25x - 6)}^{2} = {(25 \sqrt{x}) }^{2} \\ 625 {x}^{2} - 300x + 36 = 625x \\ 625 {x}^{2} - 925x + 36 = 0 \\ x = \frac{925 + \: or \: - \sqrt{ {925}^{2} - 4 \times 625 \times 36} }{2 \times 625} \\ = \frac{925 + \: or \: - 875}{1250} = 1.44 \: \: or \: \: 0.04$
x = 1.44 is not possible since sum of this with negative square root gives 6/25.

So the required number is 0.04