Math Problem Statement

14\sqrt(3)/3

Solution

The expression 1433\frac{14\sqrt{3}}{3} is already simplified. Here's some additional context:

  • 3\sqrt{3} is an irrational number, approximately equal to 1.732.
  • The fraction 1433\frac{14\sqrt{3}}{3} indicates that the entire numerator 14314\sqrt{3} is divided by 3.

If needed, the numerical value of the expression can be approximated as:

143314×1.732324.24838.083\frac{14\sqrt{3}}{3} \approx \frac{14 \times 1.732}{3} \approx \frac{24.248}{3} \approx 8.083

Let me know if you need further steps or context! 😊


Here are 5 related questions to expand your understanding:

  1. How can you rationalize the denominator of a fraction if it includes a square root?
  2. What are some properties of irrational numbers like 3\sqrt{3}?
  3. How do you simplify fractions with radicals in both the numerator and denominator?
  4. What is the approximate value of 3\sqrt{3} rounded to different decimal places?
  5. How is 3\sqrt{3} derived geometrically or algebraically?

Tip: When working with square roots in fractions, always check if rationalization or further simplification is necessary.

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Math Problem Analysis

Mathematical Concepts

Simplifying Radicals
Fractions
Irrational Numbers

Formulas

\( \frac{a\sqrt{b}}{c} \): Simplifying and approximating fractions involving radicals

Theorems

Properties of Square Roots
Properties of Rational and Irrational Numbers

Suitable Grade Level

Grades 8-10