How do you simplify #³sqrt(24w^2)# divided by #³sqrt(3w^4)#?

Question

Julia Adams · Accepted Answer

Remember that if you have roots with the same exponent their arguments can be divided under a root with that exponent.
That is
#root(a)(b)/root(a)(c) = root(a)(b/c)# For this particular example
#root(3)(24w^2)/root(3)(3w^4)# #= root(3)((24w^2)/(3w^4))# #= root(3)(8/w^2)# #= 2 root(3)(1/w^2)# #= 2/root(3)(w^2)#

Ethan Adkins · Answer

undefined To simplify ³√(24w^2) divided by ³√(3w^4), we can combine the two radicals by using the quotient rule of radicals. This rule states that the ³√(a) divided by ³√(b) is equal to the ³√(a/b).

Applying this rule to the given expression, we have:

³√(24w^2) / ³√(3w^4) = ³√(24w^2 / 3w^4)

Simplifying the expression inside the radical, we divide the coefficients and subtract the exponents of the variables:

³√(24w^2 / 3w^4) = ³√(8 / w^2)

Since 8 is a perfect cube (2^3), we can simplify further:

³√(8 / w^2) = 2 / ³√(w^2)

Therefore, the simplified form of ³√(24w^2) divided by ³√(3w^4) is 2 / ³√(w^2).