Rational Versus Irrational Numbers

Ms. Fox asked her class “Is the sum of 4.2 and radical 2 rational or irrational?” Patrick answered that the sum would be irrational. State whether Patrick is correct or incorrect. Justify your reasoning.

• The sum is rational because a rational number plus a rational number is always rational.

• The sum is irrational because the sum of an irrational number and a rational number is always irrational.

• The sum is rational because the sum of an irrational number and a rational number is always irrational.

• The sum is rational because a rational number plus an irrational number is always rational.

Tags

CCSS.HSN.RN.B.3

Determine if the product of 3√2 and 8√18 is rational or irrational. Explain your answer.

• It is irrational because the product of two irrational numbers is always irrational.

• It is rational because the product of two irrational numbers is always rational.

• It is rational because 3 times 8 is 24 and radical 2 times radical 18 is radical 36, which is 6. So it becomes 24 times 6, which is 144 (a rational number).

• It is rational because 3 times 8 is 24 and radical 2 times radical 18 is 26. This is a rational number because it can be made into a fraction.

Tags

CCSS.HSN.RN.B.3

A fraction is which type of number?

• Rational

• Irrational

• Integer

• Whole

What type of number is π ?

• Rational

• Irrational

• Integer

• Natural

Is the number rational or irrational?

• Rational

  BECAUSE IT'S A PERFECT SQUARE

  WITH A WHOLE NUMBER ANSWER

• Irrational

  BECAUSE IT'S A NON-PERFECT SQUARE

  WITH A DECIMAL ANSWER

Answer explanation

Non perfect square root!!!

Tags

CCSS.8.NS.A.1

Is the number rational or irrational?

• Rational

• Irrational

Answer explanation

NON PERFECT SQUARE ROOT: IRRATIONAL

Is the number rational or irrational?

• Rational

• Irrational

Answer explanation

This is a non-terminating decimal...it goes on forever! IRRATIONAL

Tags

CCSS.8.NS.A.1

Is this number rational or irrational?

• Rational Number

• Irrational Number

Is the number rational or irrational?

• Rational

  BECAUSE IT'S A PERFECT SQUARE

  WITH A WHOLE NUMBER ANSWER

• Irrational

  BECAUSE IT'S A NON-PERFECT SQUARE

  WITH A DECIMAL ANSWER

Answer explanation

Non perfect square root!!!

Tags

CCSS.8.NS.A.1

Is this number rational or irrational?

• Rational number

• Irrational number

Tags

CCSS.8.NS.A.1