Number Systems

Ms. Koskinas asked the class, "Is the sum of 4.2 and  $\sqrt{2}$  rational or irrational?" Ammy answered that the sum would be irrational. Is Ammy correct? Why or Why not?

• Ammy is incorrect because the sum can not be turned into a fraction. Therefore, the sum is rational. 

• Ammy is incorrect because the sum can be turned into a fraction. Therefore, the sum is rational. 

• Ammy is correct because the sum can not be turned into a fraction. Therefore, the sum is irrational. 

• Ammy is correct because the sum can be turned into a fraction. Therefore, the sum is irrational. 

Determine if the product of  $3\sqrt{2}$  and  $8\sqrt{18}$  is rational or irrational.

• Rational 

• Irrational 

Which of the following is rational?

•  $\pi$  

•  $\sqrt{17}$  

•  $\sqrt{121}$  

•  $1.3934753249....$  

Which of the following is irrational?

• $\frac{2}{3}$

• $\sqrt{3}$

• $\sqrt{49}$

• $4.8$

 Given:
L=  $\sqrt{2}$  
M=  $3\sqrt{3}$  
N=  $\sqrt{16}$  
P=  $\sqrt{9}$  
Which expression results in a rational number? 

•  $L+M$  

•  $M\times N$  

•  $N\times P$  

•  $P+L$  

Is the sum of  $3\sqrt{2}$  and  $4\sqrt{2}$  rational or irrational? Why? 

• Rational because the sum can be expressed as a fraction. 

• Rational because the sum cannot be expressed as a fraction. 

• Irrational because the sum can be expressed as a fraction. 

• Irrational because the sum cannot be expressed as a fraction.

The product of  $\sqrt{576}$  and  $\sqrt{684}$  is 

• Irrational because both factors are irrational 

• Rational because both factors are rational

• Irrational because one factor is irrational 

• Rational because one factor is rational 

Is the product of  $\sqrt{16}$  and  $\frac{4\ }{7}$  rational or irrational? 

• Rational 

• Irrational 

Which of the following is irrational?

• $\frac{1}{2}\times\sqrt{225}$

• $\frac{3}{4}\times\frac{5}{6}$

• $\sqrt{25}\times\sqrt{4}$

• $4.6+\sqrt{15}$

Which of the following is not always true?

• The sum of two rational numbers is rational.

• The product of two irrational numbers is rational.

• The sum of an irrational number and a rational number is irrational.

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