Math Problem Statement

Rationalize the denominator. \(\frac{7}{\sqrt{2}}\)

Solution

To rationalize the denominator in the expression 72\frac{7}{\sqrt{2}}, you multiply both the numerator and the denominator by 2\sqrt{2}. This process eliminates the square root from the denominator. Let's perform the calculation:

72×22=7222=722\frac{7}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{7 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{7\sqrt{2}}{2}

So, the rationalized form of 72\frac{7}{\sqrt{2}} is:

722\frac{7\sqrt{2}}{2}

Would you like more details, or do you have any questions?

Here are 5 related questions you might consider:

  1. How would you rationalize the denominator for 53\frac{5}{\sqrt{3}}?
  2. What happens when you rationalize the denominator of 15\frac{1}{\sqrt{5}}?
  3. How can you rationalize the denominator in the expression 422\frac{4}{2\sqrt{2}}?
  4. What is the result of rationalizing the denominator of 67\frac{6}{\sqrt{7}}?
  5. How would you simplify 93×33\frac{9}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}?

Tip: Rationalizing the denominator is useful because it simplifies expressions and makes them easier to work with, especially when adding or subtracting fractions.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rationalization

Formulas

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

Theorems

Rationalization of Denominators

Suitable Grade Level

Grades 8-10