Solve the Equation: Square Root of 90 Divided by Square Root of x Equals 3

The quotient property of square roots states that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. This property only works when both a and b are positive, which they are in this problem.

Squaring eliminates the square root because $(\sqrt{something})^2 = something$. However, always check your answer since squaring can sometimes introduce extra solutions that don't work in the original equation.

Yes! You could multiply both sides by $\sqrt{x}$ first to get $\sqrt{90} = 3\sqrt{x}$, then divide by 3 and square both sides. Both methods give x = 10.

Substitute x = 10 back into the original equation: $\frac{\sqrt{90}}{\sqrt{10}} = \frac{\sqrt{90}}{\sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}} = \frac{\sqrt{900}}{10} = \frac{30}{10} = 3$ ✓

Remember we're solving for x in the denominator. When $\frac{90}{x} = 9$, we get x = 10. The 90 in the numerator stays constant - we're finding what value of x makes the whole fraction equal to 9.