Which of the following is irrational? Responses 52.781654292 52.781654292 - −7 8/37 negative 7 and 8 over 37 - 3.6363636363636363... 3.6363636363636363... 3√/4, why is 3√/4, the correct choice

1 answer

Let's analyze the options provided to determine which one is irrational.

  1. 52.781654292: This is a decimal number that terminates, therefore it is a rational number.

  2. 52.781654292 - 7/8: This is the result of subtracting a rational number from a rational number, which will still yield a rational number.

  3. -7: This is an integer and hence a rational number.

  4. 8/37: This is a fraction of two integers and is therefore a rational number.

  5. -3.6363636363636363...: This represents a repeating decimal (specifically, it could be interpreted as -3.636... or -3.63 with the 63 repeating). Repeating decimals are rational numbers.

  6. 3√/4 (which I assume means \(\sqrt{3}/4\)): Here, \(\sqrt{3}\) is an irrational number (since it cannot be expressed as a fraction of two integers). Dividing an irrational number by a rational number (in this case, 4) results in an irrational number.

Therefore, the correct choice is:

  • \(\sqrt{3}/4\) is the only option that is irrational.