Solve the Radical Equation: √50/√x = 5

Multiplying both sides by $\sqrt{x}$ eliminates the fraction! This transforms $\frac{\sqrt{50}}{\sqrt{x}} = 5$ into the simpler equation $\sqrt{50} = 5\sqrt{x}$.

Look for perfect square factors! Since $50 = 25 \times 2$ and 25 is a perfect square, we get $\sqrt{50} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$.

Because $\sqrt{4} = 2$! Both expressions represent the same value. In math, we often accept equivalent forms as correct answers.

Substitute back into the original equation: $\frac{\sqrt{50}}{\sqrt{2}} = \frac{5\sqrt{2}}{\sqrt{2}} = 5$ ✓. The equation balances!

Be careful! In this problem, since we're looking for $x$ under a square root, $x$ must be positive. Always check that your solution makes sense in the original equation.