RN.3 Rational & Irrational Numbers

 $\frac{2\pi^2}{\pi}$ 

 Which word best describes the simplification of the expression?

• coefficient

• continous

• irrational

• rational

How is the product of a a rational, nonzero number and an irrational number different from the product of two irrational numbers?

• 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.

A student claims that the sum of a rational number and an irrational number is always irrational. Is the claim correct?

• 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.

Which term best describes the product of $\sqrt{5\ }and\ 2$ , and why?

• 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.

If two numbers, p and q, are both rational numbers, which best describes the sum of p + q?

• 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.

 $x+z$  

Let x be a rational number not equal to zero, and let z be an irrational number, Determine whether the operation results in a value that is always rational, never rational, or sometimes rational.

• always rational
  
  

• never rational 

• sometimes rational

 $\left(3\sqrt{6}\right)\left(2\sqrt{6}\right)$  

Pete simplifies the expression above. What would be his answer if he simplified it correctly?

•  $6\sqrt{6}$  

• 36

•  $6\sqrt{12}$  

• 216

 $y=\frac{3}{8}x-5$  

Determine the slope for the above linear equation.

 $y=5x+6$  What is the slope intercept for the equation?

• 1

• 5

• -6

• 6

 $y=mx+b$  

Which represents the slope?

• y

• m

• x

• b