Simplify the following radical expression by rationalizing the denominator.

35‾‾‾√14‾‾‾√


We are tasked with simplifying the following radical expression:

\[
\frac{\sqrt{35}}{\sqrt{14}}
\]

### Step 1: Combine the square roots
Since both the numerator and denominator are under square roots, we can combine them under a single radical:

\[
\frac{\sqrt{35}}{\sqrt{14}} = \sqrt{\frac{35}{14}}
\]

### Step 2: Simplify the fraction inside the radical
Simplify \( \frac{35}{14} \) by dividing both the numerator and denominator by their greatest common divisor, which is 7:

\[
\frac{35}{14} = \frac{35 \div 7}{14 \div 7} = \frac{5}{2}
\]

Thus, we have:

\[
\sqrt{\frac{35}{14}} = \sqrt{\frac{5}{2}}
\]

### Step 3: Rationalize the denominator
To rationalize the denominator, we multiply both the numerator and denominator by \( \sqrt{2} \):

\[
\sqrt{\frac{5}{2}} = \frac{\sqrt{5} \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{\sqrt{10}}{2}
\]

### Final Answer:
The simplified expression is:

\[
\frac{\sqrt{10}}{2}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you simplify \(\frac{\sqrt{50}}{\sqrt{18}}\)?
2. What is the process of rationalizing a denominator?
3. Can you simplify \(\frac{\sqrt{72}}{\sqrt{8}}\)?
4. What happens when the numerator is a whole number and the denominator is a square root?
5. How do you simplify expressions with cube roots?

**Tip**: When rationalizing denominators, multiplying by the radical in the denominator simplifies the expression.

Simplify the following radical expression by rationalizing the denominator: \frac{\sqrt{35}}{\sqrt{14}}.

Learn how to simplify the radical expression \frac{\sqrt{35}}{\sqrt{14}} by rationalizing the denominator. This step-by-step guide covers key concepts like simplifying radicals and rationalizing denominators. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation