Question: Solve: \sqrt{x -7} = \sqrt{x} - 1

Solution:
Given,

\sqrt{x -7} = \sqrt{x} - 1

[ squaring both sides ]

or, (\sqrt{x -7})^2 = (\sqrt{x} - 1)^2

or, x -7 = (\sqrt{x})^2 - 2× \sqrt{x}×1 + 1^2

or, x - 7 = x -2\sqrt{x} +1

or, x - x = - 2\sqrt{x} + 1 +7

or, 0 + 2\sqrt{x} = 8

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

or, \sqrt{x} = 4

[ Squaring both sides ]

or, (\sqrt{x})^2 = 4^2

\therefore x = 16
= Answer