Math Problem Statement
Rationalize the denominator of 7 / sqrt(2).
Solution
The expression in the image is . This fraction contains a radical in the denominator, which is often rationalized in mathematical conventions. Let me simplify it for you.
Steps to Simplify:
- Multiply numerator and denominator by to rationalize:
Final Answer:
The simplified form of the given expression is:
Would you like further clarification or details on this process?
Here are some related questions for practice:
- How would you rationalize ?
- Why is it important to rationalize the denominator?
- What is the value of approximately?
- Simplify .
- What happens when both numerator and denominator have radicals, such as in ?
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