Irrational, Rational, and Roots

Rational vs. Irrational

CPMS 8th Grade Math Team

​Rational Numbers

​Natural numbers, whole numbers, Integers, and Rational Numbers all fall under rational numbers.

​

​What does this mean: Positive whole numbers, Zero, Negative whole numbers, fractions, mixed numbers, perfect square roots, repeating decimals and terminating decimals are all Rational Numbers.

​

Tip: Put Square Roots in the calculator, if you receive a whole number it's a Rational Number.

Multiple Choice

Which number is a Rational Number?

• $$\sqrt[]{17}$$  

• $$\sqrt[]{144}$$  

• $$2\pi$$  

• $$4+\pi$$  

Multiple Choice

Which number is a Rational Number?

• $$\sqrt[]{80}$$  

• $$\frac{5}{\pi}$$  

• 7.9432840.......

• $$-6.5$$  

​Irrational Numbers

​Decimals that does not terminate or repeat.

​

Hint:​

Non-perfect square roots (positive or negative)

​Anything with

​

​Examples:

​9.7658128....., -7.109823...., , , , ,

Multiple Choice

Which number is an Irrational Number?

• $$\sqrt[]{81}$$  

• $$7.333333$$  

• $$3\pi$$  

• $$55\ \frac{1}{2}$$  

Multiple Choice

Which number is an irrational number?

• $$-\sqrt[]{95}$$  

• $$\sqrt[]{64}$$  

• 7.8

• 0

Multiple Choice

What type of number is

$$6+\sqrt[]{25}$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$8-\sqrt[]{35}$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$\pi+\sqrt[]{36}$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$\frac{8}{4}+\sqrt[]{4}$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$-7.5$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$\frac{\sqrt[]{25}}{20}$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$7\cdot\pi$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$6+\sqrt[]{\pi}$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$\pi$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$\sqrt[]{22}$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

$$0$$  

• Rational 

• Irrational

Multiple Choice

What type of number is

1,540,953

• Rational 

• Irrational

Multiple Choice

What type of number is

$$-9.333333$$  

• Rational 

• Irrational