Quiz about Rationals and Irrationals

Question 1

Is the result rational or irrational? Explain.

Accepted Answer

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

Answer

Rational; The sum of two rationals is always rational.

Answer

Rational; The product of two rationals is always rational.

Answer

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

Question 2

Is the result rational or irrational? Explain.

Accepted Answer

Rational; The sum of two rationals is always rational.

Answer

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

Answer

Rational; The product of two rationals is always rational.

Answer

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

Question 3

Is the result rational or irrational? Explain.

Accepted Answer

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

Answer

Rational; The sum of two rationals is always rational.

Answer

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

Answer

Rational; The product of two rationals is always rational.

Question 4

Is the result rational or irrational? Explain.

Accepted Answer

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

Answer

Rational; The sum of two rationals is always rational.

Answer

Rational; The product of two rationals is always rational.

Answer

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

Question 5

Which of the following is true?

Accepted Answer

All integers are rational numbers.

Answer

A number can be both rational and irrational.

Answer

All rational numbers are integers.

Answer

When written as a decimal, an irrational number repeats.

Question 6

Which number can be added to $$\sqrt[]{3}$$ to show that the sum of an irrational number and an irrational number is not always an irrational number?

Accepted Answer

$$-\ \sqrt[]{3}$$

Answer

$$\frac{ ext{1}}{\sqrt[]{3} ext{}}$$

Answer

0

Answer

$$\sqrt[]{3}$$

Question 7

Is the result rational or irrational? Explain.

Accepted Answer

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

Answer

Rational; The sum of two rationals is always rational.

Answer

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

Answer

Rational; The product of two rationals is always rational.

Question 8

Is the result rational or irrational? Explain.

Accepted Answer

Sometimes rational, sometimes irrational; The product of two irrationals is sometimes rational, sometimes irrational

Answer

Rational; The sum of two rationals is always rational.

Answer

Sometimes rational, sometimes irrational; The sum of two irrationals is sometimes rational, sometimes irrational.

Answer

Rational; The product of two rationals is always rational.

Question 9

Is the result rational or irrational? Explain.

Accepted Answer

Rational; The product of two rationals is always rational.

Answer

Rational; The sum of two rationals is always rational.

Answer

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

Answer

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

Question 10

Is the result rational or irrational? Explain.

Accepted Answer

Rational; The sum of two rationals is always rational.

Answer

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

Answer

Rational; The product of two rationals is always rational.

Answer

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

Question 11

Is the result rational or irrational? Explain.

Accepted Answer

Rational; The product of two rationals is always rational.

Answer

Rational; The sum of two rationals is always rational.

Answer

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

Answer

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

Question 12

Is the result rational or irrational? Explain.

Accepted Answer

Rational; The product of two rationals is always rational.

Answer

Rational; The sum of two rationals is always rational.

Answer

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

Answer

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

Question 13

Is the result rational or irrational? Explain.

Accepted Answer

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

Answer

Rational; The sum of two rationals is always rational.

Answer

Rational; The product of two rationals is always rational.

Answer

Sometimes rational, sometimes irrational; The product of two irrationals is sometimes rational, sometimes irrational

Question 14

$$\sqrt{2}\cdot\sqrt{2}$$

Accepted Answer

Rational

Answer

Irrational

Question 15

$$PRODUCT\ of\ \sqrt{2}\ and\ \sqrt{18}$$

Accepted Answer

Rational

Answer

Irrational

Question 16

$$PRODUCT\ of\ \sqrt{8}\ and\ \sqrt{3}$$

Accepted Answer

Irrational

Answer

Rational

Question 17

6\sqrt{4}-2\sqrt{25}

Accepted Answer

Rational

Answer

Irrational

Question 18

What is a rational number ?

Accepted Answer

A rational number is a number that can be written as a fraction.

Answer

A rational number is a number that cannot be written as a fraction.

Answer

A rational number cannot be a repeating decimal.

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