https://file.aiquickdraw.com/mathbot/file/1726772061373eyg96bec.jpg

Let's solve the given surds from the image.

### a) \( \sqrt{11} \times \sqrt{11} \)
This simplifies using the property \( \sqrt{a} \times \sqrt{a} = a \):
\[
\sqrt{11} \times \sqrt{11} = 11
\]

### b) \( \sqrt{5} \times \sqrt{5} \times \sqrt{2} \times \sqrt{2} \)
First, pair the surds:
\[
\sqrt{5} \times \sqrt{5} = 5 \quad \text{and} \quad \sqrt{2} \times \sqrt{2} = 2
\]
Then multiply:
\[
5 \times 2 = 10
\]

### c) \( \sqrt{6} \times \sqrt{6} \times \sqrt{6} \)
Start by simplifying \( \sqrt{6} \times \sqrt{6} \), which equals \( 6 \). Now multiply that result by another \( \sqrt{6} \):
\[
6 \times \sqrt{6} = 6\sqrt{6}
\]
This cannot be simplified further, so the final answer is:
\[
6\sqrt{6}
\]

Let me know if you need further details or have any questions! Here are 5 questions to deepen understanding:

1. What property allows us to multiply surds in these examples?
2. How do you handle surds when they aren't paired with the same number?
3. What would happen if you multiplied \( \sqrt{a} \times \sqrt{b} \) where \( a \neq b \)?
4. Can you express any of these answers in decimal form?
5. What happens if you square a surd, like \( \sqrt{x}^2 \)?

**Tip:** Always simplify surds by pairing identical square roots first!

Simplify the following surds: a) √11 × √11, b) √5 × √5 × √2 × √2, c) √6 × √6 × √6

Learn how to simplify surds like √11 × √11, √5 × √5 × √2 × √2, and √6 × √6 × √6 with a step-by-step explanation. This problem covers key concepts of surd multiplication and simplification, suitable for Grades 8-10.

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