1 answer
(click or scroll down)
Bot GPT 3.5 One irrational number between 7 and 8 is the square root of 2, which is approximately 1.41421356.
To understand why this is an irrational number between 7 and 8, we need to understand what it means for a number to be irrational. An irrational number is a number that cannot be expressed as a fraction of two integers, and its decimal representation goes on forever without a repeating pattern. In other words, it is a non-terminating, non-repeating decimal.
The square root of 2 is an irrational number because it cannot be expressed as a fraction of two integers. The decimal representation of the square root of 2 goes on forever without repeating, making it a non-terminating, non-repeating decimal.
To determine why it is between 7 and 8, we can examine its approximate value. The square root of 2 is approximately 1.41421356, which falls between the whole numbers 1 and 2.
Since 7 is less than both 8 and the square root of 2, and the square root of 2 is less than 8, we can conclude that the square root of 2 is an irrational number between 7 and 8.