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# Simplifying radical expressions: two variables

A worked example of simplifying elaborate expressions that contain radicals with two variables. In this example, we simplify √(60x²y)/√(48x). Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• "why did you convert 5/4 to 1/4*5?" Adding to this question above what videos if any cover the reasons for doing this..I wish to understand it better.

Thanks
• Because it makes it easier to simplify, because some people get confused with fractions.
• Isn't the xy also divided by 4, like the five is?
Thanks
• They are all the same term. If they weren't, and the numerator was something like 5+xy you wouldn't be able to, or at least not as cleanly. If that was the case it would be 5/4+xy/4 as you indicated... but since it is all one term: 5xy, its just fine. Heres the reasoning:

5xy/4 is the same as 5xy divided by 4. Division by 4 is the same as multiplying by 1/4. When you do 5xy*1/4 you get 5/4xy. Incase that sounds a bit strange, just think what happens when you multiple 2xy by 4. You would get 8xy, works the same way for fractions!
• I have 1875x^9-48x^5, and i need to factor it. How would I do that? I am soo confused!
• First factor out the GCD:
3x^5 ( 625x^4 - 16)
The binomial is a difference of squares:
3x^5 (25x^2+4)(25x^2 - 4)
The second binomial is also a difference of squares:
3x^5 (25x^2+4)(5x+2)(5x-2)
(1 vote)
• Wouldn't x be on the outside of the radical sign because x squared is just x? I'm confused. Can someone please explain how the x's cancel kurt/divide. I re-did the question and that was the only part I had trouble with.
(1 vote)
• Sal divided the x^2 in the numerator by the x in the denominator, which leaves an x in the numerator because x^2/x is x. So x^2 isn't there anymore.
• is sqrt(a^2 + b^2) the same as sqrt(a^2) + sqrt(b^2)?
(1 vote)
• √(a²+b²) = √a² + √b²
Let's see if this works when a=3 and b= 4
So,
√(3² + 4²) must equal √3² + √4²
√9+16 must equal 3+4
√25 must equal 7
But √25 = 5
And 5≠7
So √(a²+b²) does not equal √a²+√b²
• Can't you make 5/4 into 1.25, so you just take out the fraction and turn it into a decimal
(1 vote)
• You could, but it makes it harder. It is easier to simplify sqrt(5/4) = sqrt(5)/2.
• is there a video explaining 5 root 8+ 2 root 20- root 8?
(1 vote)
• whats the difference between principal root and square root?
(1 vote)
• Principal root is the default and is the non-negative root.
sqrt(9) = 3, not -3
If the problem wants you to use the negative root, then there will be a minus in front of the radical.
- sqrt(9) = -3

Hope this helps.
FYI - Search for intro to square roots. I believe Sal defines the principal root in that vidoe.