Solve: (√81 × √4)/(√9 × √9) - Square Root Fraction Simplification

To solve the problem, we'll simplify the expression $\frac{\sqrt{81}\cdot\sqrt{4}}{\sqrt{9}\cdot\sqrt{9}}$ using square root properties and arithmetic operations.

Step 1: Simplify each square root individually:

• $\sqrt{81} = 9$, $\sqrt{4} = 2$.
• Both $\sqrt{9}$ terms are equal to 3.

Thus, the expression becomes $\frac{9 \cdot 2}{3 \cdot 3}$.

Step 2: Perform multiplication of numbers:

• Numerator: $9 \times 2 = 18$.
• Denominator: $3 \times 3 = 9$.

The expression is now $\frac{18}{9}$.

Step 3: Simplify the fraction:

• $\frac{18}{9} = 2$, after dividing both the numerator and the denominator by the GCD, which is 9.

Therefore, the solution to the problem is $2$.