1. Which of the following numbers is a rational?

A. 4/5 ****
B. square root of 27
C. 4.02002000200002...
D. Square root of 31

2. Which type of number is shown below?
0.313311333111...

A. repeating decimal
B. rational
C. irrational***
D. terminating decimal

3. Select all the rational numbers from the list.

A. square root of 2
B.8.21221112221111 ***
C. 8.333333333... ****
D. square root of 80
E. square root of 25

4. Select all the irrational numbers from the list.
A. square root of 16
B.square root of 7 ****
C. 813.1 ***
D. -9
E. 8.070070007...

5. Which of the following numbers is irrational?
A. square root of 36
B. 1/5
C. square root of 60 ***
D.6.3

PLEASE HELP!!!

1- 4/5

2- irrational
3- 8.3333.... and square root 25
4- square root 7 and 8.070070007
5- square root 60

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Sure! I'd be happy to help you with these questions.

1. To determine which of the following numbers is rational, you need to identify if the number can be expressed as a fraction (ratio) of two integers.

A. 4/5: This is a rational number because it can be expressed as a fraction of two integers. Therefore, it is rational. (Correct)

B. Square root of 27: The square root of 27 is not a rational number because it cannot be expressed as a fraction of two integers. Therefore, it is not rational.

C. 4.02002000200002...: This is not a rational number because it is a repeating decimal. Rational numbers can be expressed as terminating decimals (finite number of digits) or repeating decimals (a repeating pattern of digits). Therefore, it is not rational.

D. Square root of 31: The square root of 31 is not a rational number because it cannot be expressed as a fraction of two integers. Therefore, it is not rational.

2. To identify the type of number 0.313311333111..., observe its decimal representation.

A. Repeating decimal: The number 0.313311333111... is a repeating decimal because it has a repeating pattern of digits. Therefore, it is a repeating decimal. (Correct)

B. Rational: Repeating decimals are a subset of rational numbers, so this option is not wrong. However, since the question asks for the specific type, it is not the best answer.

C. Irrational: Irrational numbers cannot be expressed as a fraction of two integers, and this number has a repeating pattern, so it is incorrect.

D. Terminating decimal: Terminating decimals are finite with no repeating pattern, so this option is incorrect.

3. To identify the rational numbers from the list, you need to determine if they can be expressed as a fraction of two integers.

A. Square root of 2: The square root of 2 is not a rational number because it cannot be expressed as a fraction of two integers.

B. 8.21221112221111: This is a rational number because it is a terminating decimal. Terminating decimals can be expressed as a fraction of two integers. Therefore, it is rational. (Correct)

C. 8.333333333...: This is a rational number because it is a repeating decimal. Repeating decimals can also be expressed as a fraction of two integers. Therefore, it is rational. (Correct)

D. Square root of 80: The square root of 80 is not a rational number because it cannot be expressed as a fraction of two integers.

E. Square root of 25: The square root of 25 is a rational number because it can be expressed as a fraction of two integers. Therefore, it is rational. (Correct)

4. To identify the irrational numbers from the list, you need to determine if they cannot be expressed as a fraction of two integers.

A. Square root of 16: The square root of 16 is a rational number because it can be expressed as a fraction of two integers. Therefore, it is not irrational.

B. Square root of 7: The square root of 7 is an irrational number because it cannot be expressed as a fraction of two integers. Therefore, it is irrational. (Correct)

C. 813.1: 813.1 is a rational number because it is a terminating decimal. Terminating decimals can be expressed as a fraction of two integers. Therefore, it is not irrational.

D. -9: -9 is a rational number because it can be expressed as a fraction of two integers. Therefore, it is not irrational.

E. 8.070070007...: This number is not provided in the options.

5. To determine which of the following numbers is irrational, you need to identify if it cannot be expressed as a fraction of two integers.

A. Square root of 36: The square root of 36 is not an irrational number because it can be expressed as a fraction of two integers. Therefore, it is not irrational.

B. 1/5: 1/5 is a rational number because it can be expressed as a fraction of two integers. Therefore, it is not irrational.

C. Square root of 60: The square root of 60 is an irrational number because it cannot be expressed as a fraction of two integers. Therefore, it is irrational. (Correct)

D. 6.3: 6.3 is a rational number because it can be expressed as a fraction of two integers. Therefore, it is not irrational.

I hope this clarifies the concepts for you! Let me know if you have any more questions.