Question

$\sqrt{y} - 4 = 3$

Explanation:

Step1: Eliminate the square root

Square both sides of the equation $\sqrt{y} - 4 = 3$ to get rid of the square root.
$$(\sqrt{y} - 4)^2 = 3^2$$
Wait, no, actually the original equation is $\sqrt{y}-4 = 3$? Wait, looking at the image again, the equation is $\sqrt{y} - 4 = 3$? Wait, no, the user's image shows $\sqrt{y}-4 = 3$? Wait, no, the LaTeX in the image: the equation is $\sqrt{y} - 4 = 3$? Wait, no, let's re - examine. The equation is $\sqrt{y}-4 = 3$. Wait, no, maybe it's $\sqrt{y - 4}=3$? Wait, the user's image: the square root is over $y - 4$? Wait, the original problem's image: the equation is $\sqrt{y}-4 = 3$? Or $\sqrt{y - 4}=3$? Wait, the way it's written: $\sqrt{y}-4 = 3$? Wait, no, the square root symbol is over $y$, then minus 4? Wait, no, maybe the equation is $\sqrt{y - 4}=3$. Let's assume that the equation is $\sqrt{y - 4}=3$ (maybe a typo in the initial reading). Let's proceed with $\sqrt{y - 4}=3$.

To solve for $y$, we first square both sides of the equation $\sqrt{y - 4}=3$ to eliminate the square root.
$$(\sqrt{y - 4})^2=3^2$$
Which simplifies to $y - 4 = 9$.

Step2: Solve for y

Add 4 to both sides of the equation $y - 4 = 9$.
$y-4 + 4=9 + 4$
So $y = 13$.

Wait, if the equation is $\sqrt{y}-4 = 3$, then:

Step1: Isolate the square root

Add 4 to both sides of the equation $\sqrt{y}-4 = 3$.
$\sqrt{y}-4 + 4=3 + 4$
$\sqrt{y}=7$

Step2: Eliminate the square root

Square both sides: $(\sqrt{y})^2=7^2$
$y = 49$

Looking back at the image, the equation is $\sqrt{y}-4 = 3$? Wait, the image shows $\sqrt{y}-4 = 3$ (the square root is over $y$, then minus 4). So let's correct the steps:

Step1: Isolate the square root term

Add 4 to both sides of the equation $\sqrt{y}-4 = 3$.
$\sqrt{y}-4 + 4=3 + 4$
$\sqrt{y}=7$

Step2: Square both sides to solve for y

Square both sides of the equation $\sqrt{y}=7$.
$(\sqrt{y})^2=7^2$
$y = 49$

Answer:

$y = 49$ (If the equation is $\sqrt{y}-4 = 3$) or if the equation is $\sqrt{y - 4}=3$, then $y = 13$. But based on the image's formatting, it's $\sqrt{y}-4 = 3$, so the answer is $y = 49$.