Answer:
Assuming the variable is included under the radical,
-40k²√(10)
Step-by-step explanation:
[tex](-2\sqrt{20k})(5\sqrt{8k^3})[/tex]
First we will simplify the first factor,
[tex]-2\sqrt{20k}[/tex]
We will write 20 as a product of factors:
[tex]-2\sqrt{4*5k}[/tex]
We know the square root of 2 is 2, so we pull a 2 out:
[tex]-2(2)\sqrt{5k}\\\\=-4\sqrt{5k}[/tex]
Now we will simplify the second factor,
[tex]5\sqrt{8k^3}[/tex]
We will rewrite 8 as a product of factors, as well as the variable:
[tex]5\sqrt{2*4*k^2*k}[/tex]
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:
[tex]5(2)(k)\sqrt{2k}\\\\=10k\sqrt{2k}[/tex]
This gives us the product
[tex](-4\sqrt{5k})(10k\sqrt{2k})[/tex]
Multiplying the coefficients, we have
[tex]-4(10k)(\sqrt{5k})(\sqrt{2k})\\\\=-40k(\sqrt{5k})(\sqrt{2k})[/tex]
Multiplying the two radicals, we have
[tex]-40k\sqrt{5k*2k}\\\\-40k\sqrt{10k^2}[/tex]
The square root of k² is k, so we pull a k out, leaving
[tex]-40k(k)\sqrt{10}\\\\=-40k^2\sqrt{10}[/tex]
