The expression in the image you uploaded is:

$\frac{3\sqrt{20}}{2\sqrt{8}}$

Let's simplify this step by step:

Step 1: Simplify each square root.

• $\sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}$
• $\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$

Step 2: Substitute these into the original expression:

$\frac{3\sqrt{20}}{2\sqrt{8}} = \frac{3(2\sqrt{5})}{2(2\sqrt{2})} = \frac{6\sqrt{5}}{4\sqrt{2}}$

Step 3: Simplify the fraction.

$\frac{6\sqrt{5}}{4\sqrt{2}} = \frac{3\sqrt{5}}{2\sqrt{2}}$

Step 4: Rationalize the denominator.

To remove the square root from the denominator, multiply both the numerator and the denominator by $\sqrt{2}$:

$\frac{3\sqrt{5}}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{10}}{2 \times 2} = \frac{3\sqrt{10}}{4}$

Final Answer:

$\frac{3\sqrt{10}}{4}$

Let me know if you need any further clarification or steps!

Would you like more practice with similar problems?

1. Simplify: $\frac{5\sqrt{12}}{3\sqrt{18}}$
2. Simplify: $\frac{7\sqrt{15}}{5\sqrt{3}}$
3. Rationalize: $\frac{2}{\sqrt{7}}$
4. Simplify: $\frac{6\sqrt{8}}{3\sqrt{2}}$
5. Simplify: $\frac{\sqrt{50}}{\sqrt{2}}$

Tip: When simplifying square roots, always look for perfect squares to factor out!