Question

To find the product of (−2√20k)(5√8k3), first write using a single radical. Which expression is equivalent to the given product?

Answer 1

Answer:

Assuming the variable is included under the radical,

-40k²√(10)

Step-by-step explanation:

$(-2\sqrt{20k})(5\sqrt{8k^3})$

First we will simplify the first factor,

$-2\sqrt{20k}$

We will write 20 as a product of factors:

$-2\sqrt{4*5k}$

We know the square root of 2 is 2, so we pull a 2 out:

$-2(2)\sqrt{5k}\\\\=-4\sqrt{5k}$

Now we will simplify the second factor,

$5\sqrt{8k^3}$

We will rewrite 8 as a product of factors, as well as the variable:

$5\sqrt{2*4*k^2*k}$

The square root of 2 is 2, so we pull a 2 out.  Additionally, the square root of k² is k, so we pull that out:

$5(2)(k)\sqrt{2k}\\\\=10k\sqrt{2k}$

This gives us the product

$(-4\sqrt{5k})(10k\sqrt{2k})$

Multiplying the coefficients, we have

$-4(10k)(\sqrt{5k})(\sqrt{2k})\\\\=-40k(\sqrt{5k})(\sqrt{2k})$

Multiplying the two radicals, we have

$-40k\sqrt{5k*2k}\\\\-40k\sqrt{10k^2}$

The square root of k² is k, so we pull a k out, leaving

$-40k(k)\sqrt{10}\\\\=-40k^2\sqrt{10}$

Answer 2

I will assume that is the case 
The product is -10√160k^4

which simplifies to -10*4 √10k^4   = -40√10 k^4