what is the solution to the equation $sqrt{2n + 28}-4sqrt{n}=0$?\n$n = 2$\n$n = 4$\n$n = 7$\n$n = 14$

Explanation:

Step1: Isolate one of the square - root terms

Add (4\sqrt{n}) to both sides of the equation (\sqrt{2n + 28}-4\sqrt{n}=0), we get (\sqrt{2n + 28}=4\sqrt{n}).

Step2: Square both sides

((\sqrt{2n + 28})^2=(4\sqrt{n})^2), which simplifies to (2n + 28 = 16n).

Step3: Solve for (n)

Subtract (2n) from both sides: (28=16n - 2n), so (28 = 14n). Then divide both sides by 14, we have (n = 2).

Step4: Check the solution

Substitute (n = 2) into the original equation: (\sqrt{2\times2+28}-4\sqrt{2}=\sqrt{4 + 28}-4\sqrt{2}=\sqrt{32}-4\sqrt{2}=4\sqrt{2}-4\sqrt{2}=0).

Answer:

(n = 2)