Question

$\sqrt{x - 3} = \sqrt{3}$

Explanation:

Step1: Square both sides to eliminate square roots

To solve the equation \(\sqrt{x - 3}=\sqrt{3}\), we square both sides of the equation. Squaring a square root cancels out the square root operation. So, \((\sqrt{x - 3})^2 = (\sqrt{3})^2\). This simplifies to \(x - 3=3\) because squaring \(\sqrt{a}\) gives \(a\) for non - negative \(a\).

Step2: Solve for x

Now we have the linear equation \(x - 3 = 3\). To isolate \(x\), we add 3 to both sides of the equation. Using the addition property of equality, if \(a=b\), then \(a + c=b + c\). Here, \(a=x - 3\), \(b = 3\) and \(c = 3\). So, \(x-3 + 3=3 + 3\), which simplifies to \(x=6\). We should also check if this solution is valid by substituting \(x = 6\) back into the original equation. Left - hand side: \(\sqrt{6 - 3}=\sqrt{3}\), right - hand side: \(\sqrt{3}\). Since both sides are equal, \(x = 6\) is a valid solution.

Answer:

\(x = 6\)