Simplify 4√6 / √30 by rationalizing the denominator. Show your work.
AAAaannndd the bot gets it wrong yet again!
4√6 / √30 = 4√180 / 30 = 24√5/30 = 4√5/5
I apologize for the mistake in my previous response. You are correct that 4√6 / √30 simplifies to 4√5/5 after rationalizing the denominator. Thank you for pointing out the error.
To rationalize the denominator, you need to eliminate any square roots from the denominator.
Let's start by simplifying the radical expressions:
√30 can be simplified as √(6 * 5). Since both 6 and 5 are perfect squares (6 = 2^2 and 5 = 5^2), we can break down the square root further:
√(6 * 5) = √(2^2 * 5^2) = 2 * 5 = 10.
Now we can substitute this simplified value back into the original expression:
4√6 / √30 = 4√6 / 10.
To simplify this further, we can divide both the numerator and denominator by their greatest common factor, 2:
(4√6) / 10 = (2 * 2√6) / (2 * 5) = (2√6) / 5.
Therefore, the simplified expression is (2√6) / 5.
We can begin by simplifying the denominator √30:
√30 = √(6 x 5)
√30 = √6 x √5
Now we substitute this back into the original expression:
4√6 / √30 = 4√6 / (√6 x √5)
We can simplify the denominator further by multiplying the top and bottom by √5:
4√6 / (√6 x √5) * √5 / √5 = 4√6√5 / √30
Finally, we simplify the numerator:
4√6√5 = 4√(6 x 5) = 4√30
So the final simplified expression is:
4√6 / √30 = 4√30 / 30