Math Problem Statement

112/3√

Solution

The expression 1123\frac{112}{\sqrt{3}} can be simplified by rationalizing the denominator. This involves eliminating the square root from the denominator.

Step-by-step simplification:

  1. Multiply both the numerator and the denominator by 3\sqrt{3} to remove the square root in the denominator: 1123×33=112×33\frac{112}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{112 \times \sqrt{3}}{3}

  2. Multiply the numerator: 11233\frac{112\sqrt{3}}{3}

Thus, the simplified form of the expression is: 11233\frac{112\sqrt{3}}{3}

Would you like further details on rationalization or another example?

Here are 5 related questions you can explore:

  1. How do you rationalize a denominator with a cube root?
  2. What is the numerical value of 1123\frac{112}{\sqrt{3}}?
  3. How do you simplify expressions involving higher roots?
  4. What are the steps to rationalize a denominator with two terms (binomials)?
  5. What are the properties of square roots that help in simplifying expressions?

Tip: Rationalizing a denominator makes an expression easier to interpret and compute, especially in manual calculations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Rationalization
Simplifying Radicals

Formulas

Rationalizing a denominator: \( \frac{a}{\sqrt{b}} \times \frac{\sqrt{b}}{\sqrt{b}} = \frac{a\sqrt{b}}{b} \)

Theorems

Properties of square roots: \( \sqrt{a} \times \sqrt{a} = a \)
Simplification rules for radicals

Suitable Grade Level

Grades 9-11