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

Squaring both sides changes the equation! The left side becomes $6x^2$, not $6x$. Only square when you have isolated square root terms on one side.

Rationalizing means removing square roots from the denominator. Multiply both numerator and denominator by $\sqrt{6}$ to get $\frac{6\sqrt{6}}{6} = \sqrt{6}$.

Substitute back: $\sqrt{6} \cdot \sqrt{6} = \sqrt{36} = 6$. Since $\sqrt{36} = 6$, both sides equal 6, so our answer is correct!

Because we have $\sqrt{6}$ as a coefficient multiplying x. When we divide 6 by $\sqrt{6}$, we get $\sqrt{6}$, not 6.

While mathematically correct, it's better practice to rationalize denominators. Most teachers prefer the simplified form $\sqrt{6}$ as the final answer.