https://file.aiquickdraw.com/mathbot/file/1727155948462g8nz0wf7.jpg

The question asks to "rationalize the following form" involving the square root of a fraction:

\[
\sqrt{\frac{3}{8}}
\]

To rationalize this expression, follow these steps:

1. **Break the square root into two parts** using the property of square roots:
   \[
   \sqrt{\frac{3}{8}} = \frac{\sqrt{3}}{\sqrt{8}}
   \]

2. **Simplify the denominator**:
   \[
   \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
   \]
   So the expression becomes:
   \[
   \frac{\sqrt{3}}{2\sqrt{2}}
   \]

3. **Rationalize the denominator** by multiplying both the numerator and the denominator by \(\sqrt{2}\):
   \[
   \frac{\sqrt{3}}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{3} \times \sqrt{2}}{2 \times 2} = \frac{\sqrt{6}}{4}
   \]

Thus, the rationalized form of \(\sqrt{\frac{3}{8}}\) is:

\[
\frac{\sqrt{6}}{4}
\]

Would you like further details on any of these steps, or help with another problem?

Here are 5 related questions to consider:

1. How do you rationalize a denominator in general?
2. Can the same technique be applied to higher powers, like cube roots?
3. Why do we multiply by the same square root in the numerator and denominator?
4. What are other methods for simplifying square roots of fractions?
5. How would you simplify \(\sqrt{\frac{5}{12}}\)?

**Tip**: When simplifying square roots of fractions, break the fraction into the square root of the numerator and the denominator first—it makes rationalizing easier.

Rasionalkan bentuk berikut: \( \sqrt{\frac{3}{8}} \) ?

Learn how to rationalize the square root of the fraction 3/8. This solution simplifies the square root expression using key algebraic techniques like breaking up the fraction and rationalizing the denominator. Perfect for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation