RN.3 Rational & Irrational Numbers

coefficient

continous

irrational

rational

The product of a rational, nonzero number and an irrational number is always irrational, but the product of 2 irrationals is sometimes rational.

The product of a rational, nonzero number and an irrational number is always irrational, but the product of 2 irrationals is never rational.

The product of a rational, nonzero number and an irrational number is never irrational, but the product of 2 irrationals is sometimes rational.

The product of a rational, nonzero number and an irrational number is never irrational, but the product of 2 irrationals is always rational.

No. The claim is incorrect because $2+\sqrt{4}=2+2=4$ , and 4 is a rational number.

No. The claim is incorrect because $2+\frac{1}{\sqrt{4}}=2+\frac{1}{2}=\frac{5}{2}$ , and $\frac{5}{2}$ is a rational number.

Yes. The claim is correct because $3\pi\ +4\pi\ =\ 7\pi$ , and $7\pi$ is an irrational number.

Yes. The claim is correct because $\sqrt{16}+\pi=4+\pi,\ and\ 4+\pi$ is an irrational number.

The product is rational because the product of an irrational number and another irrational number is sometimes rational.

The product is rational because the product of an irrational number and a nonzero rational number is always rational.

The product is irrational because the product of an irrational number and a nonzero rational number is irrational.

The product is irrational because the product of an irrational number and another irrational number is never rational.

The sum of p +q will always be rational.

The sum of p +q will always be irrational.

The sum of p +q will never be rational.

The sum of p +q will sometimes be rational.

always rational

never rational 

sometimes rational

 $6\sqrt{6}$  

36

 $6\sqrt{12}$  

216

1

5

-6

6

y

m

x

b