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which of the following is irrational numbers

the square root of 16
85
37

11 answers

An irrational number is a number that cannot be expressed as a fraction of two integers, and it has a non-repeating, non-terminating decimal expansion.

Now, let's analyze the options you provided:

  1. The square root of 16 is 4, which is a rational number (it can be expressed as the fraction 4/1).

  2. 85 is also a rational number (it can be expressed as the fraction 85/1).

  3. 37 is again a rational number (it can be expressed as the fraction 37/1).

None of the numbers listed (the square root of 16, 85, and 37) are irrational. All of them are rational numbers. Thus, there are no irrational numbers among your options.

11/16
- square root of 9
-square root of 49

Let's evaluate the numbers you've provided to determine which are irrational:

  1. 11/16: This is a rational number because it can be expressed as a fraction of two integers (11 and 16).

  2. -√9: The square root of 9 is 3, so -√9 = -3. This is also a rational number because it can be expressed as -3/1.

  3. -√49: The square root of 49 is 7, so -√49 = -7. This is also a rational number since it can be expressed as -7/1.

All three numbers (11/16, -√9, and -√49) are rational numbers. None of them are irrational.

which of the following is an irrational number
square root of 23
-78
square root of 41

To identify which of the given numbers is irrational, let's evaluate each option:

  1. Square root of 23 (√23): This is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal representation is non-terminating and non-repeating (approximately 4.795).

  2. -78: This is a rational number because it can be expressed as -78/1, which is the ratio of two integers.

  3. Square root of 41 (√41): This is also an irrational number, similar to √23. Its decimal form is approximately 6.403, which is non-terminating and non-repeating.

Thus, among the options provided, both square root of 23 (√23) and square root of 41 (√41) are irrational numbers. The only rational number in your list is -78.

which of the following is an irrational number
square root of 0
square root if 55
67/43
29.111...

Let's evaluate each of the numbers you provided to determine which one is irrational:

  1. Square root of 0 (√0): This equals 0, which is a rational number since it can be expressed as 0/1.

  2. Square root of 55 (√55): This is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal representation is approximately 7.416198, which is non-terminating and non-repeating.

  3. 67/43: This is a rational number because it is expressed as a fraction of two integers.

  4. 29.111...: This is a rational number. The notation indicates that the digits "1" repeat indefinitely (29.111111...), which can be expressed as a fraction.

So, in summary, the only irrational number among the options you provided is square root of 55 (√55).

which of the following is an irrational number
square root of 61
square root of 8
-67

Let's evaluate each of the numbers provided to determine which one is irrational:

  1. Square root of 61 (√61): This is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal representation is non-terminating and non-repeating (approximately 7.810).

  2. Square root of 8 (√8): This can be simplified to \(2\sqrt{2}\). Since \( \sqrt{2} \) is irrational, hence \( 2\sqrt{2} \) is also irrational. Therefore, √8 is also an irrational number.

  3. -67: This is a rational number because it can be expressed as -67/1, which is the ratio of two integers.

In conclusion, both square root of 61 (√61) and square root of 8 (√8) are irrational numbers. The only rational number among the options you provided is -67.

which of the following is a rational number
square root of 37
square root of 70
12/18

Let's evaluate each of the numbers you provided to identify which one is a rational number:

  1. Square root of 37 (√37): This is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal representation is non-terminating and non-repeating (approximately 6.08276).

  2. Square root of 70 (√70): This is also an irrational number for the same reason as √37. Its decimal representation is non-terminating and non-repeating (approximately 8.3666).

  3. 12/18: This is a rational number because it can be expressed as a fraction of two integers. It can also be simplified to 2/3, which is still a rational number.

Thus, among the given options, 12/18 is the rational number.