Question

Which of the following are irrational numbers A √86 B √74 C 81.40 D π

Answer 1

To determine which of the given numbers are irrational, we should first recall that an irrational number is a number that cannot be expressed as a fraction of two integers. In other words, it cannot be represented as a terminating or repeating decimal.

Let's analyze each option:

A. \( \sqrt{86} \) - This is an irrational number because 86 is not a perfect square.

B. \( \sqrt{74} \) - This is also an irrational number because 74 is not a perfect square.

C. \( 81.40 \) - This is a rational number because it can be expressed as \( \frac{8140}{100} \) and it has a terminating decimal.

D. \( \pi \) - This is an irrational number because it cannot be expressed as a fraction of two integers and its decimal representation is non-terminating and non-repeating.

Thus, the irrational numbers from the list are:
- A. \( \sqrt{86} \)
- B. \( \sqrt{74} \)
- D. \( \pi \)