Problem 121 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The simplified form of \( \sqrt{10} \cdot \sqrt{5} \) is \( \sqrt{50} \).

Step 1: Understand the Square Root Property

Know that according to the property of square roots, the square root of a product is equivalent to the product of the square roots, which can be written as: \( \sqrt{A \cdot B} = \sqrt{A} \cdot \sqrt{B} \). Here, \(A\) and \(B\) are any real numbers.

Step 2: Apply the Property to the Problem

Given in the problem is \( \sqrt{10} \cdot \sqrt{5} \). According to the property used in step 1, this can be rewritten as \( \sqrt{10 \cdot 5} \).

Step 3: Simplify the Expression

The multiplication inside the square root simplifies to \( \sqrt{50} \).