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

Be careful! You can only cancel identical terms directly. Here we have $\sqrt{5}$ in both numerator and denominator, but there are other terms too. It's safer to multiply everything out first.

Great observation! Both $\sqrt{10 \cdot 5 \cdot 2}$ and $\sqrt{5 \cdot 5 \cdot 4}$ equal $\sqrt{100}$. This happens because 10 × 5 × 2 = 5 × 5 × 4 = 100.

That's fine! If you get something like $\sqrt{50}$, you can still simplify it to $5\sqrt{2}$ by factoring out perfect squares. The key is looking for perfect square factors.

Yes, for multiplication! Use the property $\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}$. This often creates perfect squares that are easier to simplify than working with individual radicals.

Look for numbers that are squares of integers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100... In this problem, both the numerator and denominator give us $\sqrt{100} = 10$.