Question

1.) \\(\sqrt{y - 8} + 5 = 7\\)

Explanation:

Step1: Isolate the square root term

Subtract 5 from both sides of the equation $\sqrt{y - 8} + 5 = 7$ to get $\sqrt{y - 8}=7 - 5$.
Simplify the right side: $\sqrt{y - 8}=2$.

Step2: Eliminate the square root

Square both sides of the equation $\sqrt{y - 8}=2$ to obtain $(\sqrt{y - 8})^2 = 2^2$.
Simplify both sides: $y - 8 = 4$.

Step3: Solve for y

Add 8 to both sides of the equation $y - 8 = 4$: $y=4 + 8$.
Simplify the right side: $y = 12$.

Step4: Check the solution

Substitute $y = 12$ back into the original equation: $\sqrt{12 - 8}+5=\sqrt{4}+5 = 2 + 5=7$, which matches the right side. So the solution is valid.

Answer:

$y = 12$