Question

Sqrt(7-sqrt(x-3)) =2

Answer 1

$\sqrt{7-\sqrt{x-3}}=2\\7-\sqrt{x-3}=4\\-\sqrt{x-3}=-3\\\sqrt{x-3}=3\\x-3=9\\x=12$

Answer 2

To solve the equation Sqrt(7 - Sqrt(x - 3)) = 2, follow these steps:

Step 1: Isolate the inner square root expression. Step 2: Square both sides of the equation. Step 3: Solve for x. Step 4: Verify the solution.

Let's begin:

Step 1: Isolate the inner square root expression.

Sqrt(7 - Sqrt(x - 3)) = 2

First, get rid of the outer square root by squaring both sides of the equation:

Step 2: Square both sides of the equation.

(Sqrt(7 - Sqrt(x - 3)))^2 = 2^2

Simplifying:

7 - Sqrt(x - 3) = 4

Step 3: Solve for x.

Now, isolate the Sqrt(x - 3) term:

Sqrt(x - 3) = 7 - 4

Sqrt(x - 3) = 3

To get rid of the square root, square both sides again:

(x - 3) = 3^2

x - 3 = 9

Now, isolate x:

x = 9 + 3

x = 12

Step 4: Verify the solution.

Let's check if the solution x = 12 satisfies the original equation:

Sqrt(7 - Sqrt(12 - 3)) = Sqrt(7 - Sqrt(9)) = Sqrt(7 - 3) = Sqrt(4) = 2

The left-hand side equals the right-hand side when x = 12. Therefore, x = 12 is the solution to the equation.

So, the solution to the equation Sqrt(7 - Sqrt(x - 3)) = 2 is x = 12.