Question

Can the expression √7+2√10 be simplified using the distributive property?

Answer 1

Answer:

Yes,  \sqrt{2}(\sqrt{3.5}  + 2\sqrt{5} )

Step-by-step explanation:

By roots property, the roots can be re-write as multiplications or division, like this:

$\sqrt[n]{a} . \sqrt[n]{b} =\sqrt[n]{ab}$

Here, we can re-write both roots:

$\sqrt{7} = \sqrt{3.5*2}$ and $\sqrt{10}=\sqrt{2*5}$

Now we have:

$\sqrt{3.5} * \sqrt{2} + 2 * \sqrt{2} *\sqrt{10}$

And we can take out the common expression:

$\sqrt{2}(\sqrt{3.5} + 2\sqrt{5} )$ ⇒ Answer