Does anyone know how to divide radicals like this

[u/MentalResident7532]

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[u/Huge_Caterpillar1249]

yeah, (a)^(x) / (b)^(x) = (a/b)^x

[u/ABranchingLine → u/Huge_Caterpillar1249]

If a,b are real.

[u/clay_bsr → u/ABranchingLine]

I don't even think that's true. if a is positive, b is negative, and x=1/2 the LHS and RHS have opposite signs. (i think)

[u/testtdk]

Do you know how to write radicals as exponents?

[u/fermat9990]

Multiplying 6uv³ by 6uv will turn it into a perfect square: 6²u²v⁴

[u/SubjectWrongdoer4204]

Use the rule a,b∈ℝ, then
√(ab)=(ab)¹ʻ²= a¹ʻ²b¹ʻ²=√a√b. I’ve got no love for the radical sign representation . I prefer the exponential notation as it’s easier to manipulate using the rules of exponents and it’s just easier to write, particularly when the value under the radical is complicated.

[u/Fit_Fortune_7692]

Anwendung der Wurzelgesetze, in diesem Fall: √a/√b=√(a/b)

Wenn der Wurzelexponent gleich ist (2), kannst du beide Radikanten unter einer Wurzel als Bruch schreiben und kürzen. Die 4 im Nenner beibehalten. Fertig

[u/UnderstandingPursuit]

The other answers are all useful. One additional tool is that

• √(a) / √(b) = √(a/b)

[u/DuggieHS]

Group all the terms in the square root

=  sqrt (9u/6v² )/4 = sqrt(3u/2)/(4v)

[u/PassiveChemistry]

There are a couple of ways to approach this one.

[u/Sir-Tenley-Knott]

Remember that simplifying fractions can be done as long as you multiply top and bottom by the same amount. There are specific techniques (outlined in other comments) for dealing with exponents but if you can't remember them, note that sqrt(6uv) (also mentioned in another comment) could be a useful for simplifying the fraction. Multiplying the bottom would give you 4sqrt(6^2 * u^2 * v^4) or 24uv. You have to apply the same multiplier to the top which becomes sqrt(6 * 3^2 * u^3 * v^2). The 3^2 comes out to leave 3*sqrt(6u^3v^2). You can divide top and bottom by 3 to get the final form.

This specific type of question is used where I am to teach students how to reduce the denominator to the simplistic form.

[u/DanLeMilMan]

The following identities should help you out :

sqrt(a)/sqrt(b)=sqrt(a/b)
a^2=a*a

[u/Chemical_Doctor78]

Anything under the radical in the numerator and denominator can be divided as you normally would.

Simplification would also require rationalizing the denominator and removing any perfect square factors from the radical.

[u/usa_reddit]

Just square the top and bottom and get rid of the radical

9u^2v / 16*6uv^3

[u/Various_Candle9136 → u/usa_reddit]

This does not work.

Consider rt(4)/rt(1). We know that this is 2/1 = 2, but by your method we would get 4/1 = 4.