Questions: Solve for (y). [ sqrt2 y-5+4=8 ] What is the root? If there is no root, choose none. (10 frac12) (5 frac12) none (8 frac12)

Solve for (y). [ sqrt2 y-5+4=8 ] What is the root? If there is no root, choose none. (10 frac12) (5 frac12) none (8 frac12)
Transcript text: Solve for $y$. \[ \sqrt{2 y-5}+4=8 \] What is the root? If there is no root, choose none. $10 \frac{1}{2}$ $5 \frac{1}{2}$ none $8 \frac{1}{2}$
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Solution

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Solution Steps

To solve the given radical equation, we need to isolate the square root term and then square both sides to eliminate the square root. After that, we solve the resulting linear equation for \( y \).

Solution Approach
  1. Isolate the square root term by subtracting 4 from both sides.
  2. Square both sides to eliminate the square root.
  3. Solve the resulting linear equation for \( y \).
Step 1: Isolate the Square Root

Starting with the equation: \[ \sqrt{2y - 5} + 4 = 8 \] we isolate the square root by subtracting 4 from both sides: \[ \sqrt{2y - 5} = 4 \]

Step 2: Square Both Sides

Next, we square both sides to eliminate the square root: \[ (\sqrt{2y - 5})^2 = 4^2 \] which simplifies to: \[ 2y - 5 = 16 \]

Step 3: Solve for \( y \)

Now, we solve for \( y \) by adding 5 to both sides: \[ 2y = 21 \] Then, we divide by 2: \[ y = \frac{21}{2} \]

Final Answer

The solution for \( y \) is \[ \boxed{y = \frac{21}{2}} \]

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