Simplify the product. 10\sqrt{12x^(3) } . 2\sqrt{6x^(5) } full calculations please!!

Question

Simplify the product.


`10\sqrt{12x^(3) } . 2\sqrt{6x^(5) }`
full calculations please!!

Answer 1

`120x^4√(2)`

Explanation:

First we need to break down the numbers in the radicals into its factors

so

12= 3*2*2

x³=x*x*x

Which means we have

`10√(3*2*2*x*x*x)=20x√(3x)`

and

`2√(2*3*x*x*x*x*x) =2x^(2) √(6x)`

Because the radicand (the small number that goes up top) are the same we can just mulitply the two from here

which means we have

`(20x*2x^2)√(3x*6x)=40x^3√(18x^2) \\√(18x^2)=√(2*3*3*x*x) =3x√(2) \\=120x^4√(2)`