write the following in simplified radical form
sqrt 48 t^5 w^6
would it be 2sqrt24 t^5 /w^6?
48 = 2*2*12 = 2*2*2*2*3
so
sqrt48 = 4 sqrt 3
Now if you really mean
sqrt (48 t^5/w^6) instead of what you typed then
(4 * t^2/w^3)sqrt (3 t)
To simplify the given expression, sqrt(48 * t^5 * w^6), we need to break down the numbers under the square root sign into their prime factors.
First, let's break down 48 into its prime factors:
48 = 2 * 2 * 2 * 2 * 3 = 2^4 * 3
Now, let's simplify the expression:
sqrt(48 * t^5 * w^6) = sqrt((2^4 * 3) * t^5 * w^6)
Since the square root of a product is equal to the product of the square roots, we can simplify further:
sqrt((2^4 * 3) * t^5 * w^6) = sqrt(2^4) * sqrt(3) * sqrt(t^5) * sqrt(w^6)
Now, simplify each part individually:
sqrt(2^4) = 2^2 = 4
sqrt(3) remains as sqrt(3) since it has no perfect square factors
sqrt(t^5) = t^(5/2) = t^(2 + 1/2) = t^2 * sqrt(t)
sqrt(w^6) = w^(6/2) = w^(3 + 0) = w^3
Putting it all together, we have:
4 * sqrt(3) * t^2 * sqrt(t) * w^3
So, the simplified radical form of sqrt(48 * t^5 * w^6) is:
4 * sqrt(3) * t^2 * sqrt(t) * w^3