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.

Fill in the Blanks

Compute:

 $\left(\sqrt{3}\cdot\sqrt{5}\cdot\sqrt{7}\right)^2$  

Fill in the Blanks

Compute:

 $\sqrt{45}\cdot\sqrt{20}$  

Multiple Choice

Compute:

 $\frac{\sqrt{12}}{\sqrt{147}}$  

•  $\frac{2}{7}$  

•  $\frac{7}{2}$  

•  $\sqrt{\frac{2}{7}}$  

•  $\sqrt{\frac{4}{49}}$  

Fill in the Blanks

Compute:

 $\left(-2\sqrt{12}\right)\left(6\sqrt{75}\right)$  

Fill in the Blanks

Compute:

 $\frac{3\sqrt{200}}{2\sqrt{18}}$  

Multiple Choice

Compute:

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

• 1

• 2/3

• -2/3

• 0

Fill in the Blanks

Compute:

 $\sqrt{0.09}$  

Multiple Choice

Simplify:

 $\sqrt{700}$  

•  $70$  

•  $10\sqrt{7}$  

•  $\sqrt{70}$  

•  $-10\sqrt{7}$  

Multiple Choice

Simplify:

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

•  $\sqrt{4}-\sqrt{3}$  

•  $\sqrt{4}+\sqrt{3}$  

•  $2+\sqrt{3}$  

•  $2-\sqrt{3}$  

Fill in the Blanks

Compute:

 $\left(2\sqrt{45}-\sqrt{20}\right)\left(4\sqrt{20}\right)$  

Fill in the Blanks

 $\frac{12}{\sqrt{3}}$  equals the square root of what integer?

*type the integer and NOT the radical

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?

Fill in the Blanks

In this problem, we see how we can write √ n as a power of n. We will assume that n is nonnegative throughout the problem.

(a) Fill the blank: $\sqrt{n}\cdot\sqrt{n}=\text{}$  _