Question

solve.

\\\sqrt{y+4}-4=3\\

select the correct choice below and, if necessary, fill in the answer box within your choice.

a. the solution(s) is/are \\\quad\\.
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)

b. there is no solution.

Explanation:

Isolate the radical term

To solve the radical equation, we first isolate the square root term on one side of the equation.

$$ \sqrt{y+4} - 4 = 3 $$

Add \(4\) to both sides:

$$ \sqrt{y+4} = 7 $$

Square both sides

To eliminate the radical, square both sides of the equation.

$$ (\sqrt{y+4})^2 = 7^2 $$

$$ y + 4 = 49 $$

Solve for y

Subtract \(4\) from both sides to find the value of \(y\).

$$ y = 45 $$

Verify the solution

Check the proposed solution in the original equation to ensure it is not extraneous.

$$ \sqrt{45+4} - 4 = \sqrt{49} - 4 = 7 - 4 = 3 $$

Since \(3 = 3\), the solution \(y = 45\) is valid.

Answer:

• A. The solution(s) is/are 45. (Correct answer)
• B. There is no solution.