Question

I really need help with Dividing Radicals please

Answer 1

\[\frac{\sqrt{24}}{\sqrt{18}}=\frac{\sqrt{4} \times \sqrt{6}}{\sqrt{9}\times \sqrt{2}}=\frac{2\sqrt{6}}{3\sqrt{2}}\]\[\frac{2\sqrt{6}\times \sqrt{2}}{3\sqrt{2} \times \sqrt{2}}=\frac{2\sqrt{12}}{3\sqrt{4}}=\frac{4\sqrt{3}}{6}=\frac{2\sqrt{3}}{3}\]

Answer 2

There are several different ways to do this problem. One would be to factor 24 and 18; these two numbers have a common factor, which can be cancelled out. Mind giving that a try?

If done correctly, you'll get Sqrt(3) in the denominator. We need to "rationalize" the denominator, so that we'll have an integer (not a radical) in it. Returning to your previous result, multiply both numerator and denominator by Sqrt(3). What does that give you?

Solomon's response looks good. However, I think the problem can be done through fewer steps. Again I ask you to determine what factor is common to both 18 and 24.

Answer 3

Thankyou so much @SolomonZelman your a life saver! these radicals get on my nerves sometimes. The common factor of 18 and 24 is 6 @mathmale

Answer 4

you guys both are awesome i'd like to see both ways though :)

Answer 5

Nope, I am a mentor not a lifesavior.

Answer 6

Right, so you'd end up with Sqrt(4) / Sqrt(3) and then need only to rationalize the denominator. Solomon, your modesty is very becoming.

Answer 7

you welcome!

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Answer 8

Well thanks for the Mentoring @SolomonZelman !

Answer 9

Anytime! You can call me lifesavior if you want to, it sounds better than mentor.

Answer 10

great I see the way it can be done simpler now @mathmale but I do prefer doing it in many steps in my opinion it explains itself more clearly the long way but thank you so much the both of you for your help :)

Alright lol @SolomonZelman life saver it is :)

Answer 11

Yes, whatever you prefer.

(remember get rid of radicals in denominator)