Math Problem Statement

Rationalize the expression \(\frac{4}{\sqrt{3}}\).

Solution

The problem shown in the image asks to rationalize the expression 43\frac{4}{\sqrt{3}}.

Steps to Rationalize:

  1. Multiply the numerator and denominator by 3\sqrt{3}: 43×33=43(3)2\frac{4}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{4\sqrt{3}}{(\sqrt{3})^2}

  2. Simplify: Since (3)2=3(\sqrt{3})^2 = 3, the expression becomes: 433\frac{4\sqrt{3}}{3}

Thus, the rationalized form of 43\frac{4}{\sqrt{3}} is: 433\frac{4\sqrt{3}}{3}

Would you like more details or have any questions?

Here are 5 related questions:

  1. How do you rationalize an expression with a cube root in the denominator?
  2. What is the significance of rationalizing the denominator in mathematics?
  3. How would you rationalize 52\frac{5}{\sqrt{2}}?
  4. Can the numerator also contain a square root during rationalization?
  5. How would you handle the rationalization if the denominator had a binomial expression like 1+21 + \sqrt{2}?

Tip: When rationalizing the denominator, multiplying by the conjugate is useful if there is a binomial expression like a+ba + \sqrt{b}.

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Math Problem Analysis

Mathematical Concepts

Rationalization
Square Roots
Algebra

Formulas

Multiply by \(\frac{\sqrt{3}}{\sqrt{3}}\)
\((\sqrt{3})^2 = 3\)

Theorems

Rationalization of Denominators

Suitable Grade Level

Grades 9-10