Math Problem Statement
Solution
The mathematical expression in the image is:
Simplification Process:
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Simplify the fraction inside the square root:
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Write the expression as:
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Simplify :
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Substitute back:
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Rationalize the denominator: Multiply numerator and denominator by :
Final Answer:
Would you like further clarifications or step-by-step elaboration?
5 Related Questions:
- What does it mean to "rationalize the denominator" and why is it done?
- How can square roots of fractions be simplified efficiently?
- What is the relationship between simplifying square roots and factoring?
- How do you simplify expressions involving square roots in the numerator and denominator?
- Can be evaluated as a decimal approximation?
Tip:
Always simplify the fraction inside the square root first, as it often reduces the complexity of calculations!
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Math Problem Analysis
Mathematical Concepts
Simplification of Fractions
Square Roots
Rationalizing Denominators
Formulas
\(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)
\(\sqrt{n \cdot m} = \sqrt{n} \cdot \sqrt{m}\)
Rationalizing: \(\frac{1}{\sqrt{n}} \cdot \frac{\sqrt{n}}{\sqrt{n}} = \frac{\sqrt{n}}{n}\)
Theorems
Properties of Square Roots
Simplification Rules for Radicals
Suitable Grade Level
Grades 9-10