Rational vs Irrational and Perfect Squares

Rational and Irrational Numbers LESSON

By Kimberly George

All Real Numbers can be plotted on a number line. Real Numbers include the set of all rational numbers and the set of all irrational numbers. Which of the following numbers listed are not rational?

​Draw a line to connect each number to it's proper category:

 A RATIONAL NUMBER is a number that can be written as a fraction. An IRRATIONAL NUMBER is a number that cannot be written as a fraction of two integers a/b.

​RATIONAL

IR​RATIONAL

​2/3

​

3.5

​

√​4

​

​π

​√2

​

2.3454128904

​

√​50

​

​-9

​

​Answer B:

I know that the ​√20 is irrational because it cannot be written as a fraction because it is converted to a _______________ decimal .​

​Answer A:

I know that the ​√20 is rational because it can be written as a fraction when it's converted from a ___________________ decimal.​

​HOW WOULD YOU CLASSIFY THE √20?

I DO

 Terminating decimal (a decimal that does not go on forever) and repeating decimals are RATIONAL NUMBERS. Undefined or a non-terminating decimal is IRRATIONAL. Perfect Squares are RATIONAL NUMBERS. Non-perfect squares are IRRATIONAL.

​

​Answer B:

I know that the ​√64 is irrational because it cannot be written as a fraction because it is converted to a _______________ decimal .​

​Answer A:

I know that the ​√64 is rational because it can be written as a fraction when it's converted from a ___________________ decimal.​

​HOW WOULD YOU CLASSIFY THE √64?

WE DO

​

Terminating decimal (a decimal that does not go on forever) and repeating decimals are RATIONAL NUMBERS. Undefined or a non-terminating decimal is IRRATIONAL. Perfect Squares are RATIONAL NUMBERS. Non-perfect squares are IRRATIONAL.

​

​Answer B:

I know that the ​√28 is irrational because it cannot be written as a fraction because it is converted to a _______________ decimal .​

​Answer A:

I know that the ​√28 is rational because it can be written as a fraction when it's converted from a ___________________ decimal.​

​HOW WOULD YOU CLASSIFY THE √28?

YOU DO

​

Terminating decimal (a decimal that does not go on forever) and repeating decimals are RATIONAL NUMBERS. Undefined or a non-terminating decimal is IRRATIONAL. Perfect Squares are RATIONAL NUMBERS. Non-perfect squares are IRRATIONAL.

Rational and Irrational Numbers LESSON​

By Kimberly George

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