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
\(\frac{12+3 \sqrt{12} }{-8}\)
