Which of the following is an irrational number between 5 and 7: 6–√, 12−−√, 27−−√, 36−−√?(1 point)
The irrational number between 5 and 7 is √27
some people like to type this as 27--√
trying to get the line over the number.
Apologies for the confusion. You are correct. The irrational number between 5 and 7 is $\sqrt{27}$, or in the format you mentioned, $27-\sqrt{}$.
What is the largest integer whose square root is an irrational number between 3 and 4?(1 point)
To determine which of the given options is an irrational number between 5 and 7, we need to determine if any of them can be expressed as a terminating decimal or a repeating decimal.
Let's evaluate each option:
1. 6–√ is not an irrational number as it can be simplified to 5, which is a whole number and thus rational.
2. 12−−√ is not an irrational number either; this can be simplified to 4√3, which is also rational.
3. 27−−√ can be simplified to 3√3. Since the square root of 3 is irrational, this option is an irrational number.
4. 36−−√ can be simplified to 6, which is a whole number and thus rational.
So, the only option that is an irrational number between 5 and 7 is 27−−√.
To determine which of the given numbers is an irrational number between 5 and 7, we need to understand what an irrational number is. An irrational number is a real number that cannot be expressed as a ratio of two integers. It cannot be written as a fraction or a finite decimal and its decimal representation goes on indefinitely without repeating.
Let's check each of the given numbers:
1. 6–√: This expression represents 6 minus the square root (√) of something. However, since the square root does not have any value specified, we cannot determine whether it is rational or irrational. So, we cannot say if 6–√ is an irrational number.
2. 12−−√: Similarly, this expression represents 12 minus the square root (√) of something. Without knowing the specific value inside the square root, we cannot determine if it is rational or irrational. Hence, we cannot say if 12−−√ is an irrational number.
3. 27−−√: This expression represents 27 minus the square root (√) of something. As with the previous expressions, without knowing the value inside the square root, we cannot determine if it is rational or irrational. So, we cannot say if 27−−√ is an irrational number.
4. 36−−√: Again, this expression represents 36 minus the square root (√) of something. Without knowing the value inside the square root, we cannot determine if it is rational or irrational. Therefore, we cannot say if 36−−√ is an irrational number.
In conclusion, based on the given information, we cannot determine which of the given numbers is an irrational number between 5 and 7.