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

To solve this problem, we'll apply the properties of square roots and some straightforward algebraic techniques:

Step 1: Recall the equation given is:

$\frac{\sqrt{90}}{\sqrt{x}} = 3$

Use the property of the square root quotient:

$\sqrt{\frac{90}{x}} = 3$

Step 2: To eliminate the square root, square both sides of the equation:

$\left(\sqrt{\frac{90}{x}}\right)^2 = 3^2$

Thus, we have:

$\frac{90}{x} = 9$

Step 3: Solve for $x$ by performing algebraic manipulation:

Multiply both sides by $x$ to remove the fraction:

$90 = 9x$

Divide both sides by 9 to isolate $x$:

$x = \frac{90}{9}$

Simplifying, we find:

$x = 10$

Therefore, the solution to the equation is $x = 10$.