Problem 121 - College Algebra

Question

Explain how to simplify \(\sqrt{10} \cdot \sqrt{5}\)

Step-by-Step Solution

Answer

The simplification of \(\sqrt{10} \cdot \sqrt{5}\) is \(5 \sqrt{2}\)

Step 1: Multiply the numbers under the square root sign

Multiply the numbers 10 and 5 that are under the square root sign. This gives us \(\sqrt{10 \times 5}\), which equals \(\sqrt{50}\).

Step 2: Simplify the square root

Simplify \(\sqrt{50}\) by searching for the greatest perfect square that divides 50. This number is 25, which square root is 5. So, we can rewrite \(\sqrt{50}\) as \(\sqrt{25 \times 2}\) or as \(5 \sqrt{2}\).