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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