Question9. Explain why rewriting $\sqrt{50}$ as $\sqrt{25} \cdot \sqrt{2}$ helps you simplify $\sqrt{50}$, but rewriting $\sqrt{50}$ as $\sqrt{10} \cdot \sqrt{5}$ does not.

Studdy Solution
The key to effective simplification is identifying a factorization that includes a perfect square.
Rewriting $\sqrt{50}$ as $\sqrt{25} \cdot \sqrt{2}$ simplifies the expression because $\sqrt{25}$ is a perfect square.
Rewriting $\sqrt{50}$ as $\sqrt{10} \cdot \sqrt{5}$ does not simplify the expression because neither factor is a perfect square.
The simplification works effectively when a perfect square is involved, leading to a simpler expression.