Which of the following
is an irrational number -1 5/29 0.343434 √2/3 or 87.9821
The irrational number among the options you provided is √2/3. Non-repeating decimals like 0.343434 are rational, and the rest of the options are integers or fractions, which are also rational numbers.
An irrational number is a number that cannot be expressed as a fraction or a ratio of two integers. To determine which of the given numbers is irrational, we need to check if it can be written as a fraction.
-1 can be expressed as -1/1, which is a fraction. Therefore, -1 is not an irrational number.
Similarly, 5/29 can be written as a fraction, so it is not an irrational number.
0.343434 is a repeating decimal, but it can be expressed as a fraction. It is equivalent to 38/111. Therefore, it is not an irrational number.
√2/3 is the ratio of the square root of 2 to 3. The square root of 2 cannot be expressed as a fraction, so this is an irrational number.
Finally, 87.9821 is a rational number since it can be expressed as a fraction with a terminating decimal.
So, the only number in the given options that is an irrational number is √2/3.