An example of an irrational number between 9 and 11 is √10.
To explain this, we need to first understand what an irrational number is. An irrational number is a number that cannot be expressed as the quotient (fraction) of two integers, and it cannot be expressed as a repeating or terminating decimal. In simpler terms, an irrational number cannot be written as a simple fraction or as a finite decimal.
√10, which is the square root of 10, is an irrational number. We can see this by attempting to express it as a fraction or a decimal.
If we try to express √10 as a fraction, we cannot find two integers that can be divided to give us exactly √10. Therefore, it cannot be expressed as a simple fraction.
If we try to express √10 as a decimal, we get approximately 3.16227766. However, this decimal representation goes on infinitely without repeating or terminating. Therefore, it cannot be expressed as a finite decimal.
Since √10 cannot be expressed as a fraction or as a finite decimal, it is indeed an irrational number. As √10 is approximately 3.16227766, it falls between 9 and 11.
Show an example of an irrational number between 9 and 11.
Explain how.
5 answers
What is the least integer whose square root is an irrational number between 5 and 7?
Explain how.
Explain how.
The least integer whose square root is an irrational number between 5 and 7 is 6.
To explain this, we need to understand that an irrational number is a number that cannot be expressed as a simple fraction or as a finite decimal. In this case, we are looking for the least integer whose square root falls between 5 and 7.
If we calculate the square root of 6, we get approximately 2.449489742783178. This decimal representation goes on infinitely without repeating or terminating, which confirms that it is an irrational number.
Now, let's examine the integers less than 6. The square root of 4 is 2, which is not between 5 and 7. Similarly, the square root of 5 is approximately 2.23606797749979, which is less than 5. Therefore, the least integer whose square root is an irrational number between 5 and 7 is 6.
To explain this, we need to understand that an irrational number is a number that cannot be expressed as a simple fraction or as a finite decimal. In this case, we are looking for the least integer whose square root falls between 5 and 7.
If we calculate the square root of 6, we get approximately 2.449489742783178. This decimal representation goes on infinitely without repeating or terminating, which confirms that it is an irrational number.
Now, let's examine the integers less than 6. The square root of 4 is 2, which is not between 5 and 7. Similarly, the square root of 5 is approximately 2.23606797749979, which is less than 5. Therefore, the least integer whose square root is an irrational number between 5 and 7 is 6.
What is the least integer whose square root is an irrational number between 5 and 7?
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The least integer whose square root is an irrational number between 5 and 7 is 6.
1 answer