Could some kind, saintly soul help me solve this problem?

Simplify:

8w sqrt(48w^5) - x^2 sqrt(3xw^2)

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=8w(√16)(√3)(√w^4)(√w) - x^2(√3)(√x)(√w^2)
=32w^3(√3w) - wx^2(√3x)

not much of a "simplification" really

8w sqrt(16*3w^5) - x^2 w sqrt(3x)
= 32 w sqrt 3 * w^(5/2) - w x^2 sqrt 3 *sqrt x
= w*sqrt 3 [32 w^(5/2) - x^(5/2)]

To simplify the given expression, you can follow these steps:

1. Start by breaking down the square root terms using the property √(ab) = √a * √b.

8w * sqrt(48w^5) - x^2 * sqrt(3xw^2)
= 8w * sqrt(16) * sqrt(3) * sqrt(w^4) * sqrt(w) - x^2 * sqrt(3) * sqrt(x) * sqrt(w^2)
= 8w * 4 * sqrt(3) * w^2 * sqrt(w) - x^2 * sqrt(3) * sqrt(x) * w

2. Simplify the square root terms inside the brackets.

= 32w^3 * sqrt(3w) - wx^2 * sqrt(3x)

3. Simplify further if possible.

Unfortunately, in this case, there is not much more simplification that can be done. The simplified form of the expression is:

= 32w^3 * sqrt(3w) - wx^2 * sqrt(3x)