Numbers Between Rational Numbers Practice
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Question
Which of the following is an irrational number between 5 and 7: 6–√, 12−−√, 27−−√, 36−−√?(1 point)
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The irrational number between 5 and 7 is $\sqrt{6}$.
To determine which of the following is an irrational number between 5 and 7, we need to check if any of these numbers are not rational.
Rational numbers can be expressed as fractions, decimal numbers that terminate or repeat, or whole numbers.
Let's evaluate each number given and see if any fit the criteria for being rational:
1. 6–√: This is an irrational number because it involves the square root of a non-perfect square.
2. 12−−√: This is also an irrational number because it involves the square root of a non-perfect square.
3. 27−−√: This is an irrational number because it involves the square root of a non-perfect square.
4. 36−−√: This is a rational number because it simplifies to 6, which is a whole number.
Therefore, the irrational numbers between 5 and 7 are 6–√, 12−−√, and 27−−√.