Question

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

Answer 1

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

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:

`√(7) = √(3.5*2)` and
`√(10)=√(2*5)`

Now we have:

`√(3.5) * √(2)  + 2 * √(2) *√(10)`

And we can take out the common expression:

`√(2)(√(3.5)  + 2√(5) )` ⇒ Answer