Irrational Numbers Worksheet Grade 8

📆 Updated: 1 Jan 1970
👥 Author:
🔖 Category: Number

Are you a middle school teacher or a parent looking for a comprehensive and engaging resource to help your 8th-grade students reinforce their understanding of irrational numbers? Look no further! In this blog post, we will explore the concept of irrational numbers and provide you with a selection of worksheets specifically designed to cater to the needs of your 8th-grade learners.



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Rates Worksheets 6th Grade Math Word Problem
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Rates Worksheets 6th Grade Math Word Problem
Pin It!   Rates Worksheets 6th Grade Math Word ProblemdownloadDownload PDF

Rates Worksheets 6th Grade Math Word Problem
Pin It!   Rates Worksheets 6th Grade Math Word ProblemdownloadDownload PDF

Rates Worksheets 6th Grade Math Word Problem
Pin It!   Rates Worksheets 6th Grade Math Word ProblemdownloadDownload PDF

Rates Worksheets 6th Grade Math Word Problem
Pin It!   Rates Worksheets 6th Grade Math Word ProblemdownloadDownload PDF

Rates Worksheets 6th Grade Math Word Problem
Pin It!   Rates Worksheets 6th Grade Math Word ProblemdownloadDownload PDF

Rates Worksheets 6th Grade Math Word Problem
Pin It!   Rates Worksheets 6th Grade Math Word ProblemdownloadDownload PDF

Rates Worksheets 6th Grade Math Word Problem
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Rates Worksheets 6th Grade Math Word Problem
Pin It!   Rates Worksheets 6th Grade Math Word ProblemdownloadDownload PDF

Rates Worksheets 6th Grade Math Word Problem
Pin It!   Rates Worksheets 6th Grade Math Word ProblemdownloadDownload PDF

Rates Worksheets 6th Grade Math Word Problem
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Rates Worksheets 6th Grade Math Word Problem
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What is an irrational number?

An irrational number is a real number that cannot be expressed as a simple fraction or ratio of two integers. These numbers have non-repeating, non-terminating decimal expansions and cannot be written as a finite or repeating decimal. Examples of irrational numbers include the square root of 2, the number e, and the mathematical constant pi.

Give an example of an irrational number.

One example of an irrational number is the square root of 2 (?2). It is a number that cannot be expressed as a simple fraction or ratio of integers and has an infinite, non-repeating decimal expansion.

How are irrational numbers different from rational numbers?

Irrational numbers cannot be expressed as a ratio of two integers, meaning they cannot be written in the form of a fraction. On the other hand, rational numbers can be expressed as a ratio of two integers. Additionally, irrational numbers have non-repeating, non-terminating decimal representations, while rational numbers have either terminating or repeating decimal representations.

Can irrational numbers be expressed as fractions or ratios of integers?

No, irrational numbers cannot be expressed as fractions or ratios of integers because they have non-repeating and non-terminating decimal representations. This means they cannot be written as a ratio of two integers. Irrational numbers like pi (?) and the square root of 2 (?2) are examples of numbers that cannot be expressed as fractions.

Are square roots of non-perfect squares irrational numbers?

Yes, the square roots of non-perfect squares are irrational numbers. This means that they cannot be expressed as a ratio of two integers. Examples of non-perfect squares include numbers like 2, 3, 5, 6, 7, and so on. Their square roots are infinite, non-repeating decimals that cannot be represented as fractions.

Can the decimal representation of an irrational number be recurring or terminating?

No, the decimal representation of an irrational number cannot be recurring or terminating. Irrational numbers have an infinite and non-repeating decimal expansion, meaning they do not have a pattern that repeats or terminates. This distinction sets them apart from rational numbers, which can have finite or repeating decimal representations.

How do you determine if a number is rational or irrational?

A number is rational if it can be expressed as a fraction, where the numerator and denominator are both integers and the denominator is not equal to zero. On the other hand, a number is irrational if it cannot be expressed as a fraction and has a non-repeating, non-terminating decimal expansion. Generally, if a number can be written as a simple fraction, it is rational, whereas if it cannot be expressed in this form, it is irrational.

Are there infinitely many irrational numbers between any two rational numbers?

Yes, there are infinitely many irrational numbers between any two rational numbers. This is because between any two rational numbers, there is always a vast amount of irrational numbers that can be found, as the set of irrational numbers is uncountably infinite. This means that the gap between any two rational numbers can be filled with an infinite number of irrational numbers.

Are there any patterns or rules for adding or subtracting irrational numbers?

There are no specific patterns or rules for adding or subtracting irrational numbers. The addition and subtraction of irrational numbers follow the same rules as adding and subtracting rational numbers. Simply combine like terms and perform the arithmetic operation. However, as irrational numbers have decimal expansions that do not terminate or repeat, the resulting sum or difference may also be irrational.

Can irrational numbers be multiplied or divided with rational numbers to produce another irrational number?

Yes, when an irrational number is multiplied or divided by a rational number, the result can be another irrational number. For example, multiplying the irrational number ?2 by the rational number 2 produces the irrational number 2?2. This demonstrates that operations between irrational and rational numbers can yield irrational results.

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