Question

1. \sqrt{y - 8} = -1\

type the answer in the box below if there is a solution. if there is no solution, leave it blank.\
y = \boxed{}\
if there is no solution, explain why there is no solution. if there is a solution, leave this section blank.\
type your response in the space below.

Explanation:

Step1: Recall square root property

The principal square root $\sqrt{x}$ for any real number $x$ is always non-negative, meaning $\sqrt{x} \geq 0$ for all valid $x$.

Step2: Analyze the given equation

The equation is $\sqrt{y-8} = -1$. The left side $\sqrt{y-8}$ must be $\geq 0$, but the right side is $-1$, a negative number. A non-negative value cannot equal a negative value.

Answer:

There is no solution. The principal square root of a real number is always non-negative, so it cannot equal -1.