The expression $123\sqrt{2}$ simplifies as follows:

1. Exact Form: $123\sqrt{2}$

2. Approximate Value: The square root of 2 is approximately 1.414. Therefore: $123\sqrt{2} \approx 123 \times 1.414 = 173.961$

Final Answer:

• Exact: $123\sqrt{2}$
• Approximation: $173.96$

Would you like further details or have any questions?

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Related Questions:

1. How is $\sqrt{2}$ derived, and why is it irrational?
2. What are some real-world applications of $\sqrt{2}$?
3. Can $123\sqrt{2}$ be represented geometrically?
4. How can you compute $\sqrt{2}$ more precisely using numerical methods?
5. How does $\sqrt{2}$ relate to the Pythagorean theorem?

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Tip: To get a more precise approximation of $\sqrt{2}$, use a calculator or expand its decimal places further.