What is the product of two irrational numbers?

The product of two irrational numbers can be either rational or irrational.

If $$\sqrt{a} + \sqrt{b}$$ is rational, what can be said about $$a$$ and $$b$$ ?

Both $$a$$ and $$b$$ must be perfect squares.

What is the product of $$\sqrt{36}$$ and $$\sqrt{80}$$ ?

$$\sqrt{36} \cdot \sqrt{80} = \sqrt{2880}$$ , which is irrational.

What is the product of $$\sqrt{196}$$ and $$\sqrt{169}$$ ?

$$\sqrt{196} \cdot \sqrt{169} = 14 \cdot 13 = 182$$ , which is rational.

What is the product of $$\sqrt{8}$$ and $$\sqrt{16}$$ ?

$$\sqrt{8} \cdot \sqrt{16} = \sqrt{128}$$ , which is irrational.

Real Numbers Foundation Practice: N.RN.3 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a rational number?

Back

2.

FLASHCARD QUESTION

Front

What is an irrational number?

Back

3.

FLASHCARD QUESTION

Front

What is the square root of a perfect square?

Back

4.

FLASHCARD QUESTION

Front

What is the square root of a non-perfect square?

Back

5.

FLASHCARD QUESTION

Front

What is the sum of two rational numbers?

Back

The sum of two rational numbers is always a rational number.

6.

FLASHCARD QUESTION

Front

What is the sum of a rational number and an irrational number?

Back

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

7.

FLASHCARD QUESTION

Front

What is the product of two rational numbers?

Back

The product of two rational numbers is always a rational number.

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