Questions: Which of the following is an irrational number? √29 0 . 1257 -1/2 0

Transcript text: Which of the following is an irrational number? $\sqrt{29}$ $0 . \overline{1257}$ $-\frac{1}{2}$ 0

Solution

Solution Steps

To determine which of the given numbers is irrational, we need to understand the definition of an irrational number. An irrational number cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers. Among the options provided, we will check each one to see if it can be expressed as a fraction. The square root of a non-perfect square is typically irrational.

Step 1: Identify the Numbers

We are given the following numbers to evaluate for irrationality:

$ \sqrt{29} $
$ 0.\overline{1257} $
$ -\frac{1}{2} $
$ 0 $

Step 2: Evaluate Each Number

For $ \sqrt{29} $: Since 29 is not a perfect square, $ \sqrt{29} $ is an irrational number.
For $ 0.\overline{1257} $: This is a repeating decimal, which can be expressed as a fraction, making it rational.
For $ -\frac{1}{2} $: This is a simple fraction, which is also rational.
For $ 0 $: Zero can be expressed as $ \frac{0}{1} $, thus it is rational.

Step 3: Conclusion

Among the numbers evaluated, the only irrational number is $ \sqrt{29} $.