Math Problem Statement

Rationalize the denominator of 7 / sqrt(2).

Solution

The expression in the image is 72\frac{7}{\sqrt{2}}. This fraction contains a radical in the denominator, which is often rationalized in mathematical conventions. Let me simplify it for you.

Steps to Simplify:

  1. Multiply numerator and denominator by 2\sqrt{2} to rationalize: 72×22=722\frac{7}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{7\sqrt{2}}{2}

Final Answer:

The simplified form of the given expression is: 722\frac{7\sqrt{2}}{2}

Would you like further clarification or details on this process?

Here are some related questions for practice:

  1. How would you rationalize 53\frac{5}{\sqrt{3}}?
  2. Why is it important to rationalize the denominator?
  3. What is the value of 2\sqrt{2} approximately?
  4. Simplify 95\frac{9}{\sqrt{5}}.
  5. What happens when both numerator and denominator have radicals, such as in 37\frac{\sqrt{3}}{\sqrt{7}}?

Tip:

Always check whether simplifying the radical changes the numerical result, especially in cases involving approximations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Radical Expressions
Rationalization

Formulas

a / sqrt(b) * sqrt(b) / sqrt(b) = (a sqrt(b)) / b

Theorems

Rationalization of Denominators

Suitable Grade Level

Grades 8-10