Math Problem Statement

Simplify or rationalize the expression \( \frac{3}{\sqrt{7}} \).

Solution

The expression in the image is:

37\frac{3}{\sqrt{7}}

To simplify or rationalize this expression, we can remove the square root from the denominator by multiplying both the numerator and denominator by 7\sqrt{7}:

37×77=377=377\frac{3}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{3 \cdot \sqrt{7}}{7} = \frac{3\sqrt{7}}{7}

This is the rationalized form of the expression.

Would you like more details on this process or have any further questions?

Here are some related questions:

  1. How do you rationalize a denominator with a square root?
  2. Can you rationalize a denominator with higher powers of square roots?
  3. What is the benefit of rationalizing the denominator?
  4. How does rationalizing work with cube roots or higher?
  5. How do we handle expressions like ab\frac{a}{\sqrt{b}} when both aa and bb are variables?

Tip: When rationalizing a denominator, you're essentially clearing the denominator of radicals by using a form of 1 that incorporates the radical.

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Math Problem Analysis

Mathematical Concepts

Rationalization
Square Roots
Algebraic Fractions

Formulas

\( \frac{a}{\sqrt{b}} \times \frac{\sqrt{b}}{\sqrt{b}} = \frac{a\sqrt{b}}{b} \)

Theorems

Rationalizing the denominator

Suitable Grade Level

Grades 8-10