Classify Numbers, Square Roots, and Pythagorean Theorem

Mickey Mouse is trying to identify which number is rational from his magic book. Can you help him?

• 7.8

• 3.8910349...

• √2

• π

Answer explanation

The number 7.8 is rational because it can be expressed as a fraction, 78/10. The other choices, 3.8910349..., √2, and π, are irrational numbers.

Tags

CCSS.HSN.RN.B.3

In the Disney movie 'Alice in Wonderland', Alice falls down a rabbit hole that seems to go on forever. If the length of the rabbit hole was represented by a number, which of these could it not be?

• 12%

• √2

• -11.29

Answer explanation

The correct choice is √2 because it cannot be expressed as a fraction and its decimal representation is non-repeating and non-terminating.

Tags

CCSS.6.NS.C.7

CCSS.6.NS.C.5

Donald Duck found a treasure chest with 3.1 gold coins. If he wants to express this as a quotient of integers, which option should he choose?

• 31/1

• 31/100

• 31/10

• 3.1/1

Answer explanation

3.1 can be written as the quotient of integers by dividing 31 by 10. Therefore, the correct choice is 31/10.

Tags

CCSS.5.NBT.A.3

CCSS.5.NBT.B.7

CCSS.5.NF.B.3

• It is rational because it can be written as a decimal.

• It is irrational because it is negative.

• It is irrational because it can be written as a repeating decimal, -4.8333333.

Answer explanation

The number -4 5/6 is rational because it can be written as a quotient of integers, -29/6.

Tags

CCSS.HSN.RN.B.3

• It is rational because one of the addends is irrational.

• It is rational because both of the addends are rational.

• It may be rational or irrational, because one of the addends is irrational.

• It may be rational or irrational, because both of the addends are rational.

Answer explanation

The sum is rational because both addends are rational.

Tags

CCSS.HSN.RN.B.3

Answer explanation

The number 8.06√53 is irrational because it is the product of a rational factor (8.06) and an irrational factor (√53).

Tags

CCSS.HSN.RN.B.3

Answer explanation

The expression -3 1/2 + √36 is rational because it is the sum of two rational addends.

Tags

CCSS.HSN.RN.B.3

• +

• =

• <

• >

Answer explanation

The symbol '>' makes the sentence true because -√7 is less than -3.5.

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

• +

• =

• <

• >

Answer explanation

The symbol '<' makes the sentence true because the square root of 2 is less than 1.7320508...

Tags

CCSS.8.EE.A.2

CCSS.8.NS.A.1

CCSS.8.NS.A.2

In a Disney trivia game, Mickey Mouse asked: 'If the magic number is the square root of 10, which number should I choose to make sure my magic number is greater?'

• 3.5

• 31%

Answer explanation

The correct choice is 31% because it is the only option that is greater than the square root of 10.

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1