Question
Find an irrational number between 7 and 8. Explain your answer.
Answers
GPT 3.5
One irrational number between 7 and 8 is √2 +7.
To explain this, we know that the square root of 2 (√2) is an irrational number, meaning it cannot be expressed as a fraction or as a finite decimal.
Adding 7 to √2 provides us with a new irrational number between 7 and 8. The result is still irrational because adding a rational number (7) to an irrational number (√2) does not change the irrationality of the sum.
Therefore, the number √2 + 7 is an irrational number between 7 and 8.
To explain this, we know that the square root of 2 (√2) is an irrational number, meaning it cannot be expressed as a fraction or as a finite decimal.
Adding 7 to √2 provides us with a new irrational number between 7 and 8. The result is still irrational because adding a rational number (7) to an irrational number (√2) does not change the irrationality of the sum.
Therefore, the number √2 + 7 is an irrational number between 7 and 8.