Square both sides of the equation $\sqrt { y + 5 } = \sqrt { 5 y + 2 } - 2$ and then simplify.
A) $y + 5 = 5 y + 6$
B) $y + 5 = 5 y + 6 - \sqrt { 5 y + 2 }$
C) $y + 5 = 5 y + 6 - 4 \sqrt { 5 y + 2 }$
D) $y + 5 = 5 y$

Question

Quizplus · Accepted Answer

Squaring both sides of the equation $\sqrt { y + 5 } = \sqrt { 5 y + 2 } - 2$ gives $y + 5 = (\sqrt { 5 y + 2 } - 2)^2$. Expanding the right side yields $y + 5 = 5 y + 2 - 4\sqrt { 5 y + 2 } + 4$, which simplifies to $y + 5 = 5 y + 6 - 4\sqrt { 5 y + 2 }$.

Square Both Sides of the Equation y+5=5y+2−2\sqrt { y + 5 } = \sqrt { 5 y + 2 } - 2y+5​=5y+2​−2

Square Both Sides of the Equation $\sqrt { y + 5 } = \sqrt { 5 y + 2 } - 2$