Question

What is the following product? (StartRoot 12 EndRoot + StartRoot 6 EndRoot) (StartRoot 6 EndRoot minus StartRoot 10 EndRoot)

Answer 1

Answer:

x = 4 ± \sqrt{19}

Step-by-step explanation:

Answer 2

Answer:

The product results in: $6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}$, which agrees with answer A of the given choices.

Step-by-step explanation:

We need to apply distributive property for the product of two expressions each consisting of two terms, and also use the properties of products of radicals of the same root:

$(\sqrt{12} +\sqrt{6} )(\sqrt{6} -\sqrt{10} )=\\=\sqrt{12*6} -\sqrt{12*10} +\sqrt{6*6} -\sqrt{6*10} =\\=\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60}$

and now, we extract as many factors we can from the roots to reduce them:

$\sqrt{72} -\sqrt{120} +\sqrt{36} -\sqrt{60} =\\=6\,\sqrt{2} -2\,\sqrt{30} +6-2\,\sqrt{15}$