Question

solve for y, where y is a real number.
-1 + √(y + 8) = 2
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.

Explanation:

Step1: Isolate the square root term

Add 1 to both sides of the equation \(-1 + \sqrt{y + 8} = 2\) to get \(\sqrt{y + 8}=2 + 1\).
Simplify the right side: \(\sqrt{y + 8}=3\).

Step2: Eliminate the square root

Square both sides of the equation \(\sqrt{y + 8}=3\) to obtain \(y + 8 = 3^2\).
Calculate \(3^2\): \(y + 8 = 9\).

Step3: Solve for y

Subtract 8 from both sides of \(y + 8 = 9\): \(y=9 - 8\).
Simplify: \(y = 1\).

Step4: Check the solution

Substitute \(y = 1\) back into the original equation: \(-1+\sqrt{1 + 8}=-1+\sqrt{9}=-1 + 3 = 2\), which matches the right side. So the solution is valid.

Answer:

\(y = 1\)