https://file.aiquickdraw.com/mathbot/file/17285408740980anka9ws.jpg

The problem is asking to simplify the expression:

\[
\frac{8}{3 \sqrt{12}}
\]

Let's go step by step:

1. Simplify the square root of 12:
   \[
   \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
   \]

2. Substitute this back into the expression:
   \[
   \frac{8}{3 \sqrt{12}} = \frac{8}{3 \times 2\sqrt{3}} = \frac{8}{6\sqrt{3}} = \frac{4}{3\sqrt{3}}
   \]

3. Rationalize the denominator by multiplying the numerator and denominator by \(\sqrt{3}\):
   \[
   \frac{4}{3\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt{3}}{3 \times 3} = \frac{4\sqrt{3}}{9}
   \]

Thus, the simplified form of the expression is:

\[
\frac{4\sqrt{3}}{9}
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How do you simplify an expression with a square root in the denominator?
2. What is the process for rationalizing a denominator?
3. How do you simplify square roots of non-perfect squares?
4. What happens when you multiply a fraction by a form of 1 (like \(\frac{\sqrt{3}}{\sqrt{3}}\))?
5. How do square roots behave under multiplication?

**Tip:** When simplifying expressions with square roots, look for perfect squares within the radicand to simplify the root first!

Bentuk sederhana dari \( \frac{8}{3\sqrt{12}} \) adalah ....

This page explains how to simplify the expression \( \frac{8}{3\sqrt{12}} \) step-by-step. Learn how to handle square roots, rationalize the denominator, and reduce the fraction to its simplest form. 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