Which of the following is irrational?(1 point) Responses 3√4 Start Fraction Start Root 3 End Root over 4 End Fraction 3.6363636363636363... 3.6363636363636363... −7837 negative 7 Start Fraction 8 over 37 End Fraction 52.781654292

Question

Please simplify

Answer 1

To identify which of the given options is irrational, let's analyze each of them:

1. \( \sqrt{4} \): This equals 2, which is a rational number.

2. \( \frac{\sqrt{3}}{4} \): Here, \( \sqrt{3} \) is an irrational number, and dividing an irrational number by a non-zero rational number results in an irrational number. Thus, \( \frac{\sqrt{3}}{4} \) is irrational.

3. 3.6363636363636363...: This represents a repeating decimal (3.63 with the "63" repeating). Repeating decimals are rational numbers. Thus, this is a rational number.

4. −7837: This is an integer, which is a rational number.

5. \( \frac{8}{37} \): This is a fraction of two integers, so it is a rational number.

6. 52.781654292: This is a finite decimal number, which is also a rational number.

From the analysis, \( \frac{\sqrt{3}}{4} \) is the only irrational number among the given options.