Solve the Square Root Equation: Finding X in √6x = √36

To solve the equation $\sqrt{6}x = \sqrt{36}$, we will proceed with the following steps:

• Step 1: Simplify the square root on the right-hand side.
  $\sqrt{36} = 6$.
• Step 2: Substitute the simplified value back into the equation to obtain:
  $\sqrt{6}x = 6$.
• Step 3: Solve for $x$ by isolating the variable. Divide both sides by $\sqrt{6}$:
  $x = \frac{6}{\sqrt{6}}$.
• Step 4: Simplify the fraction:
  Multiply the numerator and denominator by $\sqrt{6}$:
  $x = \frac{6 \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}} = \frac{6 \sqrt{6}}{6} = \sqrt{6}$.

Therefore, the solution to the equation is $x = \sqrt{6}$.