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Common Core: 8th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 8th Grade Math

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All Common Core: 8th Grade Math Resources

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Example Questions

Example Question #21 : The Number System

Which of the following answer choices displays an irrational number?

Possible Answers:

$\sqrt{9}$

$\sqrt{4}$

$\sqrt{3}$

Correct answer:

$\sqrt{3}$

Explanation:

Our answer choices consist of two types of numbers: rational numbers and irrational numbers. In order to correctly answer this question, we need to know the difference between the two types of numbers.

Rational numbers are numbers that we use most often, and can be written as a simple fraction.

Irrational numbers cannot be written as fractions, and are numbers that have decimal places that never repeat or end.

In this case, $\sqrt{3}$ is our only irrational number because it cannot be written as a simple fraction.

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Example Question #22 : Understand The Difference Between Rational And Irrational Numbers: Ccss.Math.Content.8.Ns.A.1

Which of the following answer choices displays an irrational number?

Possible Answers:

84.5

$\frac{1}{5}$

$\sqrt{25}$

87.742133...

Correct answer:

87.742133...

Explanation:

Rational numbers are numbers that we use most often, and can be written as a simple fraction.

Irrational numbers cannot be written as fractions, and are numbers that have decimal places that never repeat or end.

In this case, 87.742133... is our only irrational number because it cannot be written as a simple fraction.

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Example Question #22 : The Number System

Which of the following answer choices displays an irrational number?

Possible Answers:

$\sqrt{17}$

13.13

$\frac{7}{9}$

Correct answer:

$\sqrt{17}$

Explanation:

Rational numbers are numbers that we use most often, and can be written as a simple fraction.

Irrational numbers cannot be written as fractions, and are numbers that have decimal places that never repeat or end.

In this case, $\sqrt{17}$ is our only irrational number because it cannot be written as a simple fraction.

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Example Question #23 : The Number System

Which of the following answer choices displays an irrational number?

Possible Answers:

$\frac{1}{2}$

0.25

$\sqrt{2}$

Correct answer:

$\sqrt{2}$

Explanation:

Rational numbers are numbers that we use most often, and can be written as a simple fraction.

Irrational numbers cannot be written as simple fractions, and are numbers that have decimal places that never repeat or end.

In this case, $\sqrt{2}$ is our only irrational number because it cannot be written as a simple fraction.

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Example Question #1 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Which point on the number line best represents $\sqrt{107}?$

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we can think of perfect squares around $\sqrt{107}$

$\sqrt{100}=10$

$\sqrt{121}=11$

This means that $\sqrt{107}$ has to be between and on the number line, but closer to because 107 is closer to 100 than 121 . Based on the number line provided, point L is the best representation of $\sqrt{107}$

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Example Question #2 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Which point on the number line best represents $\sqrt{2}?$

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we first need to know what number $\sqrt{2}$ represents:

$\sqrt{2}=1.41421..$

We are looking for a point on the number line that is between and , about right between them. Based on the number line provided, point A is the best representation of $\sqrt{2}$

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Example Question #3 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Which point on the number line best represents $\sqrt{4}?$

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we first need to know what number $\sqrt{4}$ represents:

We are looking for a point on the number line that is on . Based on the number line provided, point B is the best representation of $\sqrt{4}$

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Example Question #4 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Which point on the number line best represents $\sqrt{16}?$

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we first need to know what number $\sqrt{16}$ represents:

We are looking for a point on the number line that is on . Based on the number line provided, point D is the best representation of $\sqrt{16}$

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Example Question #5 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Which point on the number line best represents $\sqrt{20}?$

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we can think of perfect squares around $\sqrt{20}$

$\sqrt{16}=4$

$\sqrt{25}=5$

This means that $\sqrt{20}$ has to be between and on the number line. Based on the number line provided, point E is the best representation of $\sqrt{20}$

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Example Question #24 : The Number System

Which point on the number line best represents $\sqrt{43}?$

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we can think of perfect squares around $\sqrt{43}$

$\sqrt{36}=6$

$\sqrt{49}=7$

This means that $\sqrt{43}$ has to be between and on the number line. Based on the number line provided, point F is the best representation of $\sqrt{43}$

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All Common Core: 8th Grade Math Resources

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Common Core: 8th Grade Math : The Number System

Study concepts, example questions & explanations for Common Core: 8th Grade Math

All Common Core: 8th Grade Math Resources

Example Questions

Example Question #21 : The Number System

Example Question #22 : Understand The Difference Between Rational And Irrational Numbers: Ccss.Math.Content.8.Ns.A.1

Example Question #22 : The Number System

Example Question #23 : The Number System

Example Question #1 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Example Question #2 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Example Question #3 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Example Question #4 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Example Question #5 : Compare The Size Of Irrational Numbers And Place Them On A Number Line: Ccss.Math.Content.8.Ns.A.2

Example Question #24 : The Number System

All Common Core: 8th Grade Math Resources

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