Show an example of an irrational number between 9 and 11?
One example of an irrational number between 9 and 11 is √10.
To find an irrational number between 9 and 11, we first need to understand what makes a number irrational. An irrational number cannot be written as a fraction or ratio of two integers and has an infinite decimal representation without a recurring pattern.
One well-known irrational number is π (pi), which is approximately 3.14159. However, π is not between 9 and 11.
Let's consider the square root of 10 (√10), which is an irrational number. To find a decimal approximation of √10, we can use a calculator or mathematical software. The approximate value of √10 is 3.16227766.
Since 9 < √10 < 11, we can conclude that 3.16227766 is an example of an irrational number between 9 and 11.