# How do you simplify sqrt10sqrt8?

Jun 15, 2015

 = color(red)(4sqrt5

#### Explanation:

$\sqrt{10} \sqrt{8} = \sqrt{80}$

$\sqrt{80} = \sqrt{4 . 4 . 5}$

 = color(red)(4sqrt5

Jun 17, 2015

If you ever wondered why $\sqrt{a} \sqrt{b} = \sqrt{a b}$ (for $a , b \setminus \ge q 0$), the reason follows from the commutative and associative properties of multiplication: ${\left(\sqrt{a} \sqrt{b}\right)}^{2} = \left(\sqrt{a} \sqrt{b}\right) \cdot \left(\sqrt{a} \sqrt{b}\right)$

$= \left(\sqrt{a} \sqrt{a}\right) \cdot \left(\sqrt{b} \sqrt{b}\right) = a \cdot b$.

But $\sqrt{a b}$ is the unique nonnegative number whose square is $a b$. Hence $\sqrt{a} \sqrt{b} = \sqrt{a b}$.