No as in on top it's 1+ the square root of 2

Thank you for the clarification! The expression you're referring to is:

\[
\frac{1 + \sqrt{2}}{\sqrt{5}}
\]

### Step 1: Rationalize the denominator

To rationalize the denominator, multiply both the numerator and the denominator by \(\sqrt{5}\):

\[
\frac{1 + \sqrt{2}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} = \frac{(1 + \sqrt{2}) \times \sqrt{5}}{5}
\]

### Step 2: Simplify the numerator

Distribute \(\sqrt{5}\) in the numerator:

\[
\frac{\sqrt{5} + \sqrt{10}}{5}
\]

### Denominator

The denominator of the simplified expression is \(5\).

Would you like more details or have any questions?

---

Here are some related questions for further practice:

1. How do you rationalize the denominator of a more complex fraction?
2. How do you distribute a square root across terms in a binomial?
3. What are the steps to simplify a fraction with a binomial in the numerator?
4. Can you rationalize a denominator if it is a complex number?
5. How does rationalizing affect the value of the original expression?

**Tip:** Always ensure each term in the numerator is multiplied by the factor used to rationalize the denominator.

Understand how to rationalize the denominator of the expression 1 + sqrt(2) / sqrt(5). Learn step-by-step with a detailed explanation and practice questions. Suitable for Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation