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 $\sqrt{5}$ .

Tags

CCSS.HSN.RN.B.3

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

Tags

CCSS.HSN.RN.A.2

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.

Tags

CCSS.HSN.RN.B.3

Solve.

Mathematical Equivalence

ON

Tags

CCSS.7.NS.A.1C

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

Tags

CCSS.7.NS.A.1D

The sum of a rational number and an irrational number is

• Rational

• Irrational

• Rational or Irrational

Tags

CCSS.HSN.RN.B.3

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

• True

• False

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

Any number that can be written as a fraction

• opposite

• rational number

• absolute value

Tags

CCSS.3.NF.A.1

CCSS.3.NF.A.2B