Question

Algebra II : Radical Expressions. Instructions: Rationalize each denominator.

Answer 1

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
$\sqrt{ \frac{x}{y} } = \frac{ \sqrt{x} }{ \sqrt{y} }$



1. $\frac{ \sqrt{3} }{ \sqrt{7} }$
multply by $\frac{ \sqrt{7} }{ \sqrt{7} }$
$\frac{ \sqrt{21} }{7}$

2.$\sqrt{ \frac{1}{11} } = \frac{ \sqrt{1} }{ \sqrt{11} }$ multply by $\frac{ \sqrt{11} }{ \sqrt{11} }$
$\frac{ \sqrt{11} }{11}$


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

4. $\sqrt{ \frac{14x}{y^{2}} } = \frac{ \sqrt{14x} }{ y\sqrt{5} }$ multply by $\frac{ \sqrt{5} }{ \sqrt{5} }$
$\frac{ \sqrt{70x} }{5y}$

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 $\frac{6 \sqrt[3]{4xy^{2}} }{4x^{2}y^{2}}$

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

9.  multiply by (√a+√b)/(√a+√b)
$\frac{a+ \sqrt{ab} }{a+b}$

10 multiply top an bottom by $\frac{ \sqrt{2}+ \sqrt{6} }{ \sqrt{2}+ \sqrt{6} }$
result
$\frac{12+3 \sqrt{12} }{-8}$