50x14e exponent all square root equals simplify

To simplify the expression \( \sqrt{50 \times 14e^{x}} \), follow these steps:

### Step 1: Multiply the constants under the square root.
\[ 50 \times 14 = 700 \]
So, the expression becomes:
\[
\sqrt{700 \times e^{x}}
\]

### Step 2: Apply the property of square roots to split the terms.
\[
\sqrt{700 \times e^{x}} = \sqrt{700} \times \sqrt{e^{x}}
\]

### Step 3: Simplify the terms.
- \( \sqrt{700} = \sqrt{100 \times 7} = 10 \sqrt{7} \)
- \( \sqrt{e^{x}} = e^{x/2} \)

### Final result:
\[
\sqrt{50 \times 14e^{x}} = 10 \sqrt{7} \times e^{x/2}
\]

Thus, the simplified expression is:
\[
10 \sqrt{7} \times e^{x/2}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify more complex expressions involving square roots?
2. Can you explain properties of exponents in depth?
3. What are the rules for multiplying terms under a square root?
4. How can you express \( e^{x/2} \) in other forms?
5. How do you handle nested square roots?

**Tip:** When simplifying square roots, look for perfect squares or terms you can factor out for easier computation.

Learn how to simplify the square root of 50 times 14e exponent x with a detailed step-by-step solution. This problem involves concepts of exponents and square roots, suitable for advanced high school students or those studying advanced algebra and calculus.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation