Algebra ii : radical expressions. instructions: rationalize each denominator.

Remember multiplying something by 1 doesn't change the value

also √x times √x=x

rationalize means get rid of the square root at thebottom

basically, if the bottom is x√n then multiply the whole fraction by (x√n)/(√n) to rationalize it, then simlify by finding ones

also remember the thingummy you need for problems 6, 9 and 10
(a-b)(a+b)=a^2-b^2

and remember


1.
multply by


2. multply by


3. 2/(∛3)
multiply by (∛3)/(∛3)
(2∛3)/3

4. multply by


5. ∛(4/(9x^2))=(∛4)/(∛(9x^2))
multiply by (∛(9x^2))/(∛(9x^2))
(∛(36x^2))/(9x^2)

6.  multiply top and bottom by (1+√3)/(1+√3)
(8+8√3)/(1^2-(√3)^2)=(8+8√3)/(1-3)=(8+8√3)/ (-2)=-4-4√3

7. so tired, answer is

8. multiply tp and bottom by (√x-3)/(√x-3)
((-2√x)+6)/(x-9)

9.  multiply by (√a+√b)/(√a+√b)


10 multiply top an bottom by
result

The answer is "a"radius = 12.7 unitsdiameter = radius × 212.7 units × 2 = 25.4 units