Rationalizing Square Roots: 27+9t-3t-t^2/9-3t^2-3t+t

  • Thread starter afcwestwarrior
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In summary, the conversation discusses different mathematical expressions and problems involving square roots and rationalizing them. It mentions a specific equation and factors it to find the lowest common denominator. It also talks about adding square roots and clarifies that it is not possible to add square roots of different numbers. Finally, it addresses a misunderstanding about plugging in 9 and the resulting answer.
  • #1
afcwestwarrior
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9-t/3-squared t x 3 + square t/3+square t

i get on top 27+9square t -3t-t square t/9-3square t- 3 square t + t

i forgot what happens when u rationa,ize sqaure roots like this
 
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  • #2
i need help man, anyone know how to add square roots such as 3 square root 5 + 3 square root 7,
 
  • #3
this doesn't make sense because whenever i plug in the 9 i get 3 and the answer is 6, it doesn't make sense.
 
  • #4
What does the first post say, it's not clear?
 
  • #5
Actually NONE of these make sense!
afcwestwarrior said:
9-t/3-squared t x 3 + square t/3+square t

i get on top 27+9square t -3t-t square t/9-3square t- 3 square t + t

i forgot what happens when u rationa,ize sqaure roots like this
If you aren't going to use Latex at least use parentheses to clarify- and "t^2" is clearer than "square t".
I think you mean (9- 3t)/(3-3t^2)+ t^2/(t^2+3). Can you factor 3-3t^2? Get the lowest common denominator and add.

afcwestwarrior said:
i need help man, anyone know how to add square roots such as 3 square root 5 + 3 square root 7,
[itex]3\sqrt{5}+ 3\sqrt{7}[/itex]? About the only thing you can do is factor out the three: [itex]3(\sqrt{5}+ \sqrt{7})[/itex]. There is no way to "add square roots" of different numbers.

afcwestwarrior said:
this doesn't make sense because whenever i plug in the 9 i get 3 and the answer is 6, it doesn't make sense.
Plug 9 into what? What are you talking about?
 
  • #6
i figured this one out already, i didn't mean 3 squared i meant the square root of 3
 

1. What is rationalizing square roots?

Rationalizing square roots is the process of simplifying a square root expression by removing any irrational numbers from the denominator. This is done by multiplying the expression by a suitable rational number so that all the terms in the denominator become rational numbers.

2. How do you rationalize a square root expression?

To rationalize a square root expression, you need to multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate is obtained by changing the sign between the two terms in the denominator. This will result in the elimination of the square root in the denominator, making the expression easier to simplify.

3. Can you explain the steps to rationalize the expression 27+9t-3t-t^2/9-3t^2-3t+t?

Step 1: Identify the irrational term in the denominator, which in this case is 9-3t^2.
Step 2: Rewrite the expression as (27+9t-3t-t^2)/(9-3t^2-3t+t).
Step 3: Multiply both the numerator and denominator by the conjugate of the irrational term, which is 9+3t.
Step 4: Simplify the expression by expanding and combining like terms.
Step 5: The final expression after rationalizing the square root is 27+9t-3t-t^2/9-3t^2-3t+t.

4. Why is it important to rationalize square roots?

Rationalizing square roots is important because it helps in simplifying expressions and makes it easier to perform calculations. It also helps in finding the exact value of an irrational number, which cannot be represented in decimal form. In some cases, rationalizing square roots can also help in solving equations and inequalities.

5. What are some common mistakes to avoid while rationalizing square roots?

Some common mistakes to avoid while rationalizing square roots are:
- Forgetting to multiply both the numerator and denominator by the conjugate of the irrational term.
- Incorrectly expanding and simplifying the expression.
- Forgetting to change the sign between the two terms in the denominator while finding the conjugate.
- Not simplifying the expression after rationalizing, which may result in the expression being more complex than before.

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