Adding and Multiplying Rational and Irrational Numbers

What is the value of 5√3 × √12 ?

• 30

• 6

• √180

• 15√12

√5 is an irrational number. Which of the following operations on it will give a rational number?

• adding $\sqrt{5}$ and then multiplying by $\sqrt{5}$ .

What is the value of (3 - √3) (2 - √2) ?

• 6 - √6

• 6 -2√3 - 3√2 + √6

• 6 + √6

• 6 -2√3 - 3√2 - √6

Is the result rational or irrational? Explain.

• Rational; The sum of two rationals is always rational.

• Irrational; The sum of a rational and an irrational is always irrational.

• Rational; The product of two rationals is always rational.

• Irrational; The product of a  rational and an irrational is always irrational.

Solve.

Mathematical Equivalence

ON

1.      Select each box in the table where the numbers from corresponding rows and columns will have a rational sum.

The sum of a rational number and an irrational number is

• Rational

• Irrational

• Rational or Irrational

Bob says that if he adds a rational number and an irrational number together they the result is an irrational number.

• True

• False

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.

Any number that can be written as a fraction

• opposite

• rational number

• absolute value