Rationalizing Radicals



Rationalizing Radicals

Rationalizing with ONE TERM denominators:

 

*Steps:

1. Multiply both the numerator and the denominator by a radical that will get rid of the radical in the denominator

[pic]

2. Make sure that all radicals are simplified

3. Simplify fraction

[pic]= [pic]

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Example 1:  

1. Multiply the fraction by[pic]to get rid of the radical in the denominator

[pic]

2. Simplify radicals if you can

( [pic]is already in lowest form

3. Reduce fraction if possible

( can’t reduce the fraction further so your answer is [pic]

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Example 2: [pic]

1. Multiply

[pic]

2. Simplify radicals

[pic][pic]

3. Reduce fraction

[pic]

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TRY:

1. [pic] 2. [pic] 3. [pic] 4. [pic] 5. [pic]

Rationalizing with TWO TERM denominators:

* Steps: 

1. Find the conjugate of the denominator

- find the conjugate by of a binomial by changing the sign that is between the two terms, but keep the same order of the terms

- Conjugate in the example given is [pic]

2. Multiply the numerator and the denominator of the fraction by the conjugate found in Step 1

 [pic]

- Use distribution (or FOIL) in the denominator and the middle 2 terms will cancel out every time

( [pic]

- Use distribution in the numerator as well

3. Simplify all radicals

4. Simplify the fraction if possible

- Combine like terms when possible

( REMEMBER: In order to add/ subtract radicals, you have to have the same number underneath the radical bar!

** In the example, all radicals are in simplest form and the fraction can’t be reduced so the answer is [pic]or [pic]

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Example 3: [pic]

1. Find the conjugate

( [pic]

2. Multiply the fraction by the conjugate

[pic]

3. Simplify all radicals

- [pic]cannot be simplified

4. Simplify fraction

- Remember to check for like terms

[pic]

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Example 4:

1. Find the conjugate

( ([pic])

2. Multiply the fraction by the conjugate

[pic]

3. Simplify the radicals that can be simplified

[pic]

4. Simplify the fraction

[pic]

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Example 5:

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Try:

6.   7. 8.

Math 1 Name______________________

Worksheet Rationalizing Radicals:

1. [pic] 2. [pic] 3. [pic]

4. [pic] 5. [pic] 6. [pic]

7. [pic] 8. [pic] 9. [pic]

10. [pic] 11. [pic] 12. [pic]

13. [pic] 14. [pic] 15. [pic]

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