Question

Find the simplified product:

Answer 1

Simplify the radical by breaking the radicand up into a product of known factors
The answer is B.

Answer 2

Answer:  The correct option is (B) $-30x^2\sqrt{2x}.$

Step-by-step explanation:  We are given to select the correct expression that is the simplest form of the following product:

$E=2\sqrt{5x^3}(-3\sqrt{10x^2})$

We will be using the following properties in the simplification:

$(i)~\sqrt a\times \sqrt{b}=\sqrt{ab},\\\\(ii)~a^x\times a^y=a^{x+y}.$

We have

$E\\\\=2\sqrt{5x^3}(-3\sqrt{10x^2})\\\\=2\times (-3)\sqrt{5\times 10}~x^\frac{3}{2}\times x\\\\=-6\sqrt{50}~x^{\frac{3}{2}+1}\\\\=-6\times 5\sqrt{2}~x^\frac{5}{2}\\\\=-30\sqrt{2x^5}\\\\=-30x^2\sqrt{2x}.$

Thus, the required simplified product is $-30x^2\sqrt{2x}.$

Option (B) is CORRECT.