# Explanation: ## Step1: Isolate the square root term Subtract 8 from both sides of the equation \(8 + \sqrt{y - 3}=10\). \[ \begin{align*} 8 + \sqrt{y - 3}- 8&=10 - 8\\ \sqrt{y - 3}&= 2 \end{align*} \] ## Step2: Eliminate the square root Square both sides of the equation \(\sqrt{y - 3}=2\) to get rid of the square root. \[ \begin{align*} (\sqrt{y - 3})^2&=2^2\\ y - 3&= 4 \end{align*} \] ## Step3: Solve for \(y\) Add 3 to both sides of the equation \(y - 3 = 4\). \[ \begin{align*} y-3 + 3&=4 + 3\\ y&= 7 \end{align*} \] We can check the solution by substituting \(y = 7\) back into the original equation: Left - hand side: \(8+\sqrt{7 - 3}=8+\sqrt{4}=8 + 2=10\), which is equal to the right - hand side. So \(y = 7\) is a valid solution. # Answer: \(y = 7\)

8 + √(y - 3) = 10

QUESTION IMAGE

Question

8 + √(y - 3) = 10

Explanation:

Step1: Isolate the square root term

Subtract 8 from both sides of the equation \(8 + \sqrt{y - 3}=10\).

$$ LATEXBLOCK0 $$

Step2: Eliminate the square root

Square both sides of the equation \(\sqrt{y - 3}=2\) to get rid of the square root.

$$ LATEXBLOCK1 $$

Step3: Solve for \(y\)

Add 3 to both sides of the equation \(y - 3 = 4\).

$$ LATEXBLOCK2 $$

We can check the solution by substituting \(y = 7\) back into the original equation:
Left - hand side: \(8+\sqrt{7 - 3}=8+\sqrt{4}=8 + 2=10\), which is equal to the right - hand side. So \(y = 7\) is a valid solution.

Answer:

\(y = 7\)