Questions: Which number is irrational? A. 4/3 B. 0 . 7 C. √3 D. 3.14

Transcript text: Which number is irrational? A. $\frac{4}{3}$ B. $0 . \overline{7}$ C. $\sqrt{3}$ D. 3.14

Solution

Solution Steps

To determine which number is irrational, we need to identify the number that cannot be expressed as a fraction of two integers. Among the options, the square root of a non-perfect square is typically irrational.

Step 1: Identify the Numbers

We are given four numbers to evaluate for irrationality:

$ A = \frac{4}{3} $
$ B = 0.\overline{7} $
$ C = \sqrt{3} $
$ D = 3.14 $

Step 2: Determine Rationality

A number is considered irrational if it cannot be expressed as a fraction of two integers.

$ A = \frac{4}{3} $ is a rational number because it is a fraction.
$ B = 0.\overline{7} $ is also rational, as it can be expressed as $ \frac{7}{9} $.
$ C = \sqrt{3} $ is known to be irrational because 3 is not a perfect square.
$ D = 3.14 $ is a rational number, as it can be expressed as $ \frac{314}{100} $.

Step 3: Conclusion

Among the options, the only number that is irrational is $ C = \sqrt{3} $.