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.

Learn how to solve the expression 2(45)^0.5 step-by-step with detailed explanations and a numerical approximation. This problem covers exponentiation, square roots, and the multiplication of radicals. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation