Short Answer 
The expression to simplify is √(5x)(√(8x²) Р2√x). By applying the distributive property and simplifying the resulting terms, the final simplified expression becomes 2x√(10x) Р2x√5.
Step 1: Identify the Expression
Start with the expression you need to simplify, which is the product of two square roots: √(5x)(√(8x²) Р2√x). This expression can be tackled using the distributive property. You need to recognize the terms under the radicals and how they can be combined.
Step 2: Apply the Distributive Property
Use the distributive property to multiply each term within the parentheses by the square root outside. This involves putting everything under the radicals and expressing it as:
- √(5x) * √(8x²)
- – 2‚àö(5x) * ‚àö(x)
This will give you (5x)(8x²) Р2(5x)(x), which simplifies the expression further.
Step 3: Simplify the Result
Combine and simplify the terms you’ve derived. This results in:
- 2x² * 10x for the first term.
- Р2x² * 5 for the second term.
Collect the like terms, leading to the final simplified form of 2x‚àö(10x) – 2x‚àö5, which matches choice D.