Simplify the radical expression by rationalizing the denominator.
5
-------
sqrt 30
A. 30 sqrt5
B. sqrt30
C. sqrt180 /30
D. sqrt30 /6
I did it on my own and did not come out with any of these answers, please help me.
5/√30
(5√30)/30
√30/6
Thank you
You're welcome
Well, you've certainly made quite a mess of things! Don't worry, I'll help you clean it up.
To simplify the expression 5 / sqrt(30), we can rationalize the denominator by multiplying both the numerator and denominator by sqrt(30). This will eliminate the radical in the denominator.
So, let's do it step by step:
5 / sqrt(30) * sqrt(30) / sqrt(30)
This simplifies to:
(5 * sqrt(30)) / (sqrt(30) * sqrt(30))
In the denominator, sqrt(30) * sqrt(30) is simply 30:
(5 * sqrt(30)) / 30
And we can simplify further:
sqrt(30) / 6
So, the correct answer is (D) sqrt(30) / 6.
Hope that helps you clean up your mathematical mess!
To simplify the given expression 5/sqrt(30), we need to rationalize the denominator.
Rationalizing the denominator involves multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of sqrt(30) is -sqrt(30).
So, we can rewrite the expression as:
5 * sqrt(30) / (sqrt(30) * -sqrt(30))
Simplifying the denominator, we get:
5 * sqrt(30) / -30
Now, we can simplify the numerator:
5 * sqrt(30) = sqrt(25) * sqrt(30) = sqrt(5^2) * sqrt(2 * 3 * 5) = 5 * sqrt(2 * 3 * 5) = 5 * sqrt(30)
Putting it back into the expression:
5 * sqrt(30) / -30 = -5 * sqrt(30) / 30
This simplifies to:
- sqrt(30) / 6
Therefore, the correct answer is D. sqrt(30) / 6.