Question

Simplify 4√6 / √30 by rationalizing the denominator. Show your work.

Answer 1

AAAaannndd the bot gets it wrong yet again!

4√6 / √30 = 4√180 / 30 = 24√5/30 = 4√5/5

Answer 2

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

Answer 3

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.