To solve the expression $2(45)^{0.5}$, we need to evaluate each part step-by-step.

1. Calculate the square root of 45:
   $(45)^{0.5} = \sqrt{45}$

   We know that 45 can be factored into 9 and 5: $\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}$

2. Multiply by 2:
   Now, multiply the result by 2: $2 \times 3\sqrt{5} = 6\sqrt{5}$

So, $2(45)^{0.5} = 6\sqrt{5}$.

If you want a numerical approximation: $6\sqrt{5} \approx 6 \times 2.236 \approx 13.416$

Final Answer:

$2(45)^{0.5} = 6\sqrt{5} \approx 13.416$

Would you like more details or have any questions?

Here are some related questions that might help expand your understanding:

1. How do you simplify square roots with different factors?
2. What is the process for multiplying roots with coefficients?
3. How can you estimate square roots without a calculator?
4. What are some common mistakes to avoid when simplifying square roots?
5. How does understanding prime factorization help with square roots?

Tip: Always check if a square root can be simplified by factoring into perfect squares.