Which Is The Correct Classification Of 18 \sqrt{18} 18 ​ ?A. Irrational Number, Non-repeating Decimal B. Irrational Number, Terminating Decimal C. Rational Number, Terminating Decimal D. Rational Number, Non-repeating Decimal

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Introduction

In mathematics, numbers can be classified into different categories based on their properties. One of the fundamental classifications is between rational and irrational numbers. Rational numbers are those that can be expressed as the ratio of two integers, while irrational numbers are those that cannot be expressed as a ratio of integers. In this article, we will explore the classification of $\sqrt{18}$ and determine whether it is a rational or irrational number.

What are Rational Numbers?

Rational numbers are those numbers that can be expressed as the ratio of two integers. In other words, a rational number is a number that can be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b$ is non-zero. Rational numbers include all integers, fractions, and decimals that terminate or repeat. For example, $\frac{1}{2}$, $\frac{3}{4}$, and $0.5$ are all rational numbers.

What are Irrational Numbers?

Irrational numbers are those numbers that cannot be expressed as a ratio of integers. In other words, an irrational number is a number that cannot be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b$ is non-zero. Irrational numbers include all decimals that do not terminate or repeat, such as $\pi$, $e$, and $\sqrt{2}$.

The Square Root of 18

The square root of 18, denoted by $\sqrt{18}$, is a number that, when multiplied by itself, gives 18. In other words, $\sqrt{18} \times \sqrt{18} = 18$. To determine whether $\sqrt{18}$ is a rational or irrational number, we need to examine its decimal representation.

Decimal Representation of $\sqrt{18}$

To find the decimal representation of $\sqrt{18}$, we can use a calculator or a computer program to perform the calculation. When we do this, we find that $\sqrt{18} \approx 4.24264069$. This decimal representation does not terminate or repeat, which suggests that $\sqrt{18}$ may be an irrational number.

Is $\sqrt{18}$ a Rational or Irrational Number?

Based on the decimal representation of $\sqrt{18}$, we can conclude that it is an irrational number. This is because the decimal representation does not terminate or repeat, which is a characteristic of irrational numbers. Therefore, the correct classification of $\sqrt{18}$ is an irrational number.

Why is $\sqrt{18}$ an Irrational Number?

$\sqrt{18}$ is an irrational number because it cannot be expressed as a ratio of integers. In other words, there is no integer $a$ and non-zero integer $b$ such that $\sqrt{18} = \frac{a}{b}$. This is because the decimal representation of $\sqrt{18}$ does not terminate or repeat, which means that it cannot be expressed as a finite decimal or a repeating decimal.

Conclusion

In conclusion, the correct classification of $\sqrt{18}$ is an irrational number. This is because the decimal representation of $\sqrt{18}$ does not terminate or repeat, which is a characteristic of irrational numbers. Therefore, the correct answer is A. Irrational number, non-repeating decimal.

Final Thoughts

Understanding the classification of numbers is an important aspect of mathematics. By recognizing whether a number is rational or irrational, we can better understand its properties and behavior. In this article, we explored the classification of $\sqrt{18}$ and determined that it is an irrational number. This knowledge can be applied to a wide range of mathematical problems and can help us to better understand the properties of numbers.

References

• [1] "Rational and Irrational Numbers" by Math Open Reference
• [2] "Square Root of 18" by Wolfram Alpha
• [3] "Irrational Numbers" by Khan Academy

Glossary

• Rational Number: A number that can be expressed as the ratio of two integers.
• Irrational Number: A number that cannot be expressed as a ratio of integers.
• Terminating Decimal: A decimal that terminates or ends after a finite number of digits.
• Non-Repeating Decimal: A decimal that does not repeat or terminate.
• Square Root: A number that, when multiplied by itself, gives a specified value.
  

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Introduction

In our previous article, we explored the classification of $\sqrt{18}$ and determined that it is an irrational number. In this article, we will answer some frequently asked questions (FAQs) about $\sqrt{18}$ and provide additional information to help clarify its properties and behavior.

Q: What is the decimal representation of $\sqrt{18}$?

A: The decimal representation of $\sqrt{18}$ is approximately 4.24264069. This decimal representation does not terminate or repeat, which is a characteristic of irrational numbers.

Q: Is $\sqrt{18}$ a rational or irrational number?

A: $\sqrt{18}$ is an irrational number. This is because the decimal representation of $\sqrt{18}$ does not terminate or repeat, which means that it cannot be expressed as a finite decimal or a repeating decimal.

Q: Why is $\sqrt{18}$ an irrational number?

A: $\sqrt{18}$ is an irrational number because it cannot be expressed as a ratio of integers. In other words, there is no integer $a$ and non-zero integer $b$ such that $\sqrt{18} = \frac{a}{b}$. This is because the decimal representation of $\sqrt{18}$ does not terminate or repeat, which means that it cannot be expressed as a finite decimal or a repeating decimal.

Q: Can $\sqrt{18}$ be expressed as a fraction?

A: No, $\sqrt{18}$ cannot be expressed as a fraction. This is because it is an irrational number, and irrational numbers cannot be expressed as a ratio of integers.

Q: Is $\sqrt{18}$ a terminating or non-terminating decimal?

A: $\sqrt{18}$ is a non-terminating decimal. This is because its decimal representation does not terminate or end after a finite number of digits.

Q: Can $\sqrt{18}$ be expressed as a repeating decimal?

A: No, $\sqrt{18}$ cannot be expressed as a repeating decimal. This is because its decimal representation does not repeat or terminate.

Q: Is $\sqrt{18}$ a whole number?

A: No, $\sqrt{18}$ is not a whole number. This is because it is an irrational number, and irrational numbers are not whole numbers.

Q: Can $\sqrt{18}$ be expressed as a square of an integer?

A: No, $\sqrt{18}$ cannot be expressed as a square of an integer. This is because it is an irrational number, and irrational numbers cannot be expressed as a square of an integer.

Q: Is $\sqrt{18}$ a positive or negative number?

A: $\sqrt{18}$ is a positive number. This is because the square root of a number is always positive, regardless of the sign of the number.

Q: Can $\sqrt{18}$ be expressed as a multiple of an integer?

A: Yes, $\sqrt{18}$ can be expressed as a multiple of an integer. In fact, $\sqrt{18} = 3\sqrt{2}$, which is a multiple of the integer 3.

Conclusion

In conclusion, we have answered some frequently asked questions (FAQs) about $\sqrt{18}$ and provided additional information to help clarify its properties and behavior. We hope that this article has been helpful in understanding the properties of $\sqrt{18}$ and its classification as an irrational number.

References

• [1] "Rational and Irrational Numbers" by Math Open Reference
• [2] "Square Root of 18" by Wolfram Alpha
• [3] "Irrational Numbers" by Khan Academy

Glossary

• Rational Number: A number that can be expressed as the ratio of two integers.
• Irrational Number: A number that cannot be expressed as a ratio of integers.
• Terminating Decimal: A decimal that terminates or ends after a finite number of digits.
• Non-Repeating Decimal: A decimal that does not repeat or terminate.
• Square Root: A number that, when multiplied by itself, gives a specified value.
• Whole Number: A number that is not a fraction or decimal.
• Multiple: A number that can be expressed as a product of an integer and another number.