Simplify the Expression: (√10 × √5 × √2)/(√5 × √5 × √4)

Solve the following exercise:

$\frac{\sqrt{10}\cdot\sqrt{5}\cdot\sqrt{2}}{\sqrt{5}\cdot\sqrt{5}\cdot\sqrt{4}}=$

To solve this problem, we'll simplify the given expression step by step:

First, let's simplify the numerator:

$\sqrt{10} \cdot \sqrt{5} \cdot \sqrt{2} = \sqrt{10 \cdot 5 \cdot 2} = \sqrt{100}$.

Simplifying further, $\sqrt{100} = 10$.

Next, simplify the denominator:

$\sqrt{5} \cdot \sqrt{5} \cdot \sqrt{4} = \sqrt{5 \cdot 5 \cdot 4} = \sqrt{100}$.

And $\sqrt{100} = 10$.

Now, divide the simplified numerator by the simplified denominator:

$\frac{10}{10} = 1$.

Therefore, the solution to the problem is $1$.