Rationalizing the denominator

Rationalizing the denominator

Multiple Select

Which of the following are rational numbers? Check all that apply.

• 4

•  $\sqrt{4}$  

•  $\sqrt{3}\times\sqrt{3}$  

•  $\pi$  

Multiple Choice

What would you multiply

 $\sqrt{7}$  by to make it a rational number?

• 7

•  $7^2$  

• 1

•  $\sqrt{7}$  

Multiple Select

We rationalize the denominator in a fraction because...

• we love to memorize rules

• we like rational numbers.

• it is easier to divide by a rational number than an irrational number.

Fill in the Blank

When rationalizing the denominator, you are multiplying the fraction by a version of what number?

 $\frac{7}{\sqrt{2}}=\frac{7}{\sqrt{2}}\times\frac{?}{?}$  

Open Ended

For binomials with radicals, you need to know how to multiply conjugates.

What is the conjugate of  $4-\sqrt{7}$  ?

Open Ended

When mutliplying conjugates , you are applying the expansion  $\left(a+b\right)\left(a-b\right)=a^2-b^2.$  

When you apply this rule to binomials with radicals, the result is a rational number.

Multiply:
 $\left(4-\sqrt{7}\right)\left(4+\sqrt{7}\right)$ .