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To rationalize the denominator of \(\frac{10}{\sqrt{6}}\), we follow these steps:

### Step 1: Multiply both the numerator and the denominator by \(\sqrt{6}\).
\[
\frac{10}{\sqrt{6}} \times \frac{\sqrt{6}}{\sqrt{6}} = \frac{10 \times \sqrt{6}}{\sqrt{6} \times \sqrt{6}} = \frac{10\sqrt{6}}{6}
\]

### Step 2: Simplify the result.
Since there are no common factors between \(10\) and \(6\), the expression is already in its simplest form:
\[
\frac{10\sqrt{6}}{6}
\]

Thus, the rationalized form of \(\frac{10}{\sqrt{6}}\) is \(\frac{10\sqrt{6}}{6}\).

Would you like more details on this solution, or have any further questions?

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Here are 5 related questions for further practice:
1. Rationalize the denominator of \(\frac{7}{\sqrt{5}}\).
2. Simplify \(\frac{12}{\sqrt{8}}\) after rationalizing the denominator.
3. What is the result of rationalizing \(\frac{15}{\sqrt{3}}\)?
4. How would you rationalize the denominator of \(\frac{18}{\sqrt{2}}?\)
5. Rationalize and simplify \(\frac{9}{\sqrt{7}}\).

**Tip**: When rationalizing the denominator, remember you always multiply by the same square root in both numerator and denominator to eliminate the square root in the denominator.

Rationalise the denominator of 10/√6. Give your answer in its simplest form.

Learn how to rationalise the denominator of the expression 10/√6 and express the answer in its simplest form. This solution involves multiplying by a conjugate to eliminate the square root from the denominator. Suitable for students in Grades 9-11.

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