Question

divide and simplify. for any answers with a square root, simplify and write your answer in the form sqrt(___) with no spaces.

\\\frac{3\sqrt{3}}{5\sqrt{6}}\\

Explanation:

⚡ Using what you learned: Rationalizing Denominators

Step 1: Simplify the radical fraction

Divide the square roots in the numerator and denominator:

$$ \frac{3\sqrt{3}}{5\sqrt{6}} = \frac{3}{5} \cdot \sqrt{\frac{3}{6}} = \frac{3}{5} \cdot \sqrt{\frac{1}{2}} = \frac{3}{5\sqrt{2}} $$

Step 2: Rationalize the denominator

Multiply the numerator and the denominator by \(\sqrt{2}\) to eliminate the radical from the bottom:

$$ \frac{3}{5\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{3\sqrt{2}}{5 \cdot 2} = \frac{3\sqrt{2}}{10} $$

Step 3: Format the final answer

Following the instruction to write any square root in the form sqrt(__) with no spaces:

• Numerator: 3sqrt(2)
• Denominator: 10

Answer:

• Top box: 3sqrt(2)
• Bottom box: 10