I have an algebra question that says i have to simplify the fraction by rationalizing the denominator of the fraction 4 sqrt 6/sqrt 30.
problem is, idk what rationalizing is. well, i looked it up, but can someone help me rationalize the denominator of this fraction, then simplify? i received an answer yesterday, which was somewhat helpful, but when you answer, can you tell me what exactly you do to get the numbers you get?
again?
4√6/√30 * √30/√30 = 4√180/30 = 4*6√5/30 = 4√5/5
or
4√6/√30 = 4√6 / √5√6 = 4/√5 = 4√5/5
oh i see now thanks. i was confused yeterday.
Why did you repeat this post and have a tutor doing unnecessary work
when I gave you a complete solution for the same question yesterday?
https://www.jiskha.com/questions/1826193/i-have-an-algebra-question-that-says-i-have-to-simplify-the-fraction-by-rationalizing-the
i already said because i didnt understand the solution i got yesterday.
Of course! I'd be happy to help you understand rationalizing the denominator and simplify the given fraction.
To rationalize the denominator, we need to eliminate any square roots in the denominator. In this case, we have the fraction 4√6/√30.
Step 1: Simplify the square roots in the fraction if possible.
- The square root of 6 cannot be simplified further.
- The square root of 30 can be simplified as follows:
√30 = √(2 * 15) = √2 * √15 = √2 * √(3 * 5) = √2 * √3 * √5 = √6√5.
So, the original fraction can be rewritten as 4√6/(√6√5).
Step 2: Rationalize the denominator.
- Multiply the numerator and denominator by the conjugate of the denominator, which is √6√5.
- By doing so, we eliminate the square root in the denominator.
The fraction becomes (4√6 * √6√5) / (√6√5 * √6√5).
Step 3: Simplify the expression.
- In the numerator, the square roots can be multiplied to get √6 * √6 = √36.
- In the denominator, the square roots can also be multiplied to get (√6√5 * √6√5) = (√6 * √6)(√5 * √5) = 6 * 5 = 30.
The simplified expression is then (4√36) / 30.
Step 4: Further simplify the expression, if possible.
- Since √36 = 6, the final expression is (4 * 6) / 30.
Simplifying 4 * 6 gives us 24, so the final answer is 24/30.
To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 6.
- 24 ÷ 6 = 4
- 30 ÷ 6 = 5
Hence, the simplified fraction is 4/5.
Therefore, the rationalized and simplified fraction for 4√6/√30 is 4/5.