To determine which of the following numbers is irrational, let's analyze each option:
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3√4: This represents the cube root of 4, which is an irrational number because 4 is not a perfect cube.
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Start Fraction Start Root 3 End Root over 4 End Fraction: This represents \(\frac{\sqrt{3}}{4}\). Since \(\sqrt{3}\) is an irrational number, this entire expression is also irrational.
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−7837: This is a rational number because it can be expressed as a fraction (-7837/1).
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52.781654292: This is a decimal number that does not repeat or terminate, it appears to be a rational approximation but since it is presented in this context without more details, we will classify it as a potentially rational number (but may not be exactly so if it's a truncated decimal).
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3.6363636363636363...: This number is repeating (3.6363...), which indicates that it is a rational number.
Based on this analysis, the two that qualify as irrational numbers are:
- 3√4
- Start Fraction Start Root 3 End Root over 4 End Fraction
Among the options presented, both 1 and 2 contain irrational numbers. However, if you're looking for a single answer, option "Start Fraction Start Root 3 End Root over 4 End Fraction" (assuming that's how it’s represented as \(\frac{\sqrt{3}}{4}\)) would fit as an explicitly defined irrational number.