https://file.aiquickdraw.com/mathbot/file/172676389014814zswxb2.jpg

The expression shown in the image is:

\[
\frac{42}{\sqrt{45}}
\]

### Simplifying the Expression:

1. **Simplify the square root**:  
   \[
   \sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}
   \]

2. **Rewrite the expression**:  
   \[
   \frac{42}{\sqrt{45}} = \frac{42}{3\sqrt{5}} = \frac{42}{3} \times \frac{1}{\sqrt{5}} = 14 \times \frac{1}{\sqrt{5}} = \frac{14}{\sqrt{5}}
   \]

3. **Rationalize the denominator**:  
   Multiply the numerator and the denominator by \(\sqrt{5}\):
   \[
   \frac{14}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{14\sqrt{5}}{5}
   \]

Thus, the simplified form of the expression is:
\[
\frac{14\sqrt{5}}{5}
\]

Would you like further details or explanations? 

Here are some related questions to explore:
1. How do you rationalize a denominator?
2. What does it mean to simplify a square root?
3. Can the numerator be further simplified in some cases?
4. How do you handle more complex square roots like \(\sqrt{75}\)?
5. Why is rationalizing the denominator often preferred in mathematics?

**Tip**: Always check if a square root can be simplified by factoring it into smaller numbers!

Simplify the expression 42 / √45 and rationalize the denominator.

Learn how to simplify the expression 42 divided by √45 and rationalize the denominator. This detailed solution involves simplifying square roots and multiplying to remove the square root from the denominator. Suitable for students in Grades 8-10.

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