Math Problem Statement
Simplify \(\sqrt{\frac{1}{2}}\) and \(\sqrt{\frac{1}{3}}\).
Solution
The expressions in the image are:
Let’s simplify each of these.
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Simplifying : To rationalize the denominator: So, .
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Simplifying : To rationalize the denominator: So, .
Let me know if you would like further clarification on these steps.
Here are five related questions for further exploration:
- How would you simplify or other similar fractions?
- What happens if you take for different values of and ?
- How do you rationalize the denominator of ?
- How would these expressions change if the square root were cubed?
- Can you apply this simplification technique to complex fractions?
Tip: Rationalizing the denominator is a common technique to simplify expressions, making them easier to interpret in both exact and decimal forms.
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Math Problem Analysis
Mathematical Concepts
Algebra
Square Roots
Rationalization
Formulas
Square root of a fraction: \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\)
Rationalization of \(\frac{1}{\sqrt{b}}\): \(\frac{1}{\sqrt{b}} \times \frac{\sqrt{b}}{\sqrt{b}} = \frac{\sqrt{b}}{b}\)
Theorems
Properties of square roots
Suitable Grade Level
Grades 8-10