Class 4 Extensions

Class 4 Extensions

What We're Doing :)

The problems are listed roughly in order of difficulty. The earlier problems are close to the level of the class discussion, while the later problems are challenging extensions of the material.

Multiple Choice

Compute:

 $\frac{\sqrt{12}}{\sqrt{147}}$  

•  $\frac{2}{7}$  

•  $\frac{7}{2}$  

•  $\sqrt{\frac{2}{7}}$  

•  $\sqrt{\frac{4}{49}}$  

Multiple Choice

Compute:

 $\sqrt{2\ \frac{7}{9}}-\sqrt{1\ \frac{7}{9}}-1$  

• 1

• 2/3

• -2/3

• 0

Multiple Choice

Simplify:

 $\sqrt{700}$  

•  $70$  

•  $10\sqrt{7}$  

•  $\sqrt{70}$  

•  $-10\sqrt{7}$  

Multiple Choice

Simplify:

 $\frac{\sqrt{32}-\sqrt{24}}{\sqrt{8}}$  

•  $\sqrt{4}-\sqrt{3}$  

•  $\sqrt{4}+\sqrt{3}$  

•  $2+\sqrt{3}$  

•  $2-\sqrt{3}$  

Open Ended

 Jenny multiplies the square root of her favorite integer by

 $\sqrt{2}$  . The resulting product is an integer. For example, 9 could be Jenny's favorite integer because  $\sqrt{2}\cdot\sqrt{8}=\sqrt{16}=4$  , which is an integer.

(a) Name three integers that could be Jenny's favorite integer.

(b) Suppose Jenny instead divides the square root of her favorite integer by  $\sqrt{2}$  . Must the resulting quotient be an integer?