Math Problem Statement
√2Is approximately equal to 1.41 and √3 is approximately equal to 1.73. Use this idea to find two fractions between √2 and√3
Solution
To find two fractions between and , we can use the approximate values you provided: and . We can select fractions within this range.
Let's choose fractions with small denominators to make calculations easier:
- The fraction , which is slightly less than , so it doesn't work.
- The fraction , which is between and .
- The fraction , which is also between and .
- The fraction , which is slightly more than , so it doesn't work.
Thus, two fractions between and are:
These fractions satisfy the condition .
Would you like more details or have any questions?
Here are some related questions:
- What is the decimal representation of to more decimal places?
- What is the decimal representation of to more decimal places?
- How do we rationalize the denominator of a fraction?
- What is the continued fraction representation of ?
- What is the continued fraction representation of ?
- How can we find more fractions between and ?
- What are other methods to approximate square roots?
- How do we determine if a fraction is closer to or ?
Tip: When approximating square roots, using fractions with small denominators helps in making quick and simple estimates.
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Math Problem Analysis
Mathematical Concepts
Square Roots
Approximation
Fraction Representation
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9