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{ (x)/(y) } = ( √(x) )/( √(y) )`



1.
`( √(3) )/( √(7) )`
multply by
`( √(7) )/( √(7) )`

`( √(21) )/(7)`

2.
`\sqrt{ (1)/(11) } = ( √(1) )/( √(11) )` multply by
`( √(11) )/( √(11) )`

`( √(11) )/(11)`


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

4.
`\sqrt{ (14x)/(y^(2)) } = ( √(14x) )/( y√(5) )` multply by
`( √(5) )/( √(5) )`

`( √(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)

`(a+ √(ab) )/(a+b)`

10 multiply top an bottom by
`( √(2)+ √(6) )/( √(2)+ √(6) )`
result

`(12+3 √(12) )/(-8)`