show an example of a irrational number between 9 and 11
3 answers
√10 is an example of an irrational number between 9 and 11.
explain how you got the answer
To understand how the number √10 is irrational and falls between 9 and 11, we need to know what an irrational number is.
An irrational number is a number that cannot be expressed as a fraction of two integers and has an infinite decimal expansion without repeating patterns.
The square root of 10 (√10) is an example of an irrational number because it cannot be written as a fraction or a whole number. Its decimal representation goes on forever without repeating.
Now, to show that √10 falls between 9 and 11, we can approximate its decimal value.
Calculating, we know that √9 (the square root of 9) is equal to 3, and √16 (the square root of 16) is equal to 4.
Therefore, we can deduce that √10 must be greater than 3 but less than 4. So, √10 falls between the values of 9 and 11.
An irrational number is a number that cannot be expressed as a fraction of two integers and has an infinite decimal expansion without repeating patterns.
The square root of 10 (√10) is an example of an irrational number because it cannot be written as a fraction or a whole number. Its decimal representation goes on forever without repeating.
Now, to show that √10 falls between 9 and 11, we can approximate its decimal value.
Calculating, we know that √9 (the square root of 9) is equal to 3, and √16 (the square root of 16) is equal to 4.
Therefore, we can deduce that √10 must be greater than 3 but less than 4. So, √10 falls between the values of 9 and 11.
11 answers