Question: Solve: \sqrt{x +8} -2 = \sqrt{x}

Solution:
Given,

\sqrt{x +8} -2 = \sqrt{x}

or, \sqrt{x+8} = \sqrt{x} + 2

[ Squaring both sides ]

or, (\sqrt{x+8})^2 = (\sqrt{x} + 2)^2

or, x +8 = (\sqrt{x})^2 + 2×\sqrt{x}×2 + 2^2

or, x + 8 = x + 4\sqrt{x} + 4

or, x -x + 8 -4 = 4\sqrt{x}

or, 4 = 4\sqrt{x}

or, 4\sqrt{x} = 4

or, \sqrt{x} = \dfrac{4}{4}

or, \sqrt{x} = 1

or, \sqrt{x} = \sqrt{1}

\therefore x = 1
= Answer