Question

Simplify the expression. $$\sqrt{5} \cdot \sqrt{15}$$

Short answer

The simplified form of the expression \( \sqrt{5} \cdot \sqrt{15} \) is \( 5 \sqrt{3} \).

Step-by-step solution

Understand the Properties of Square Roots

One crucial property to understand this exercise is that the product of two square roots is equal to the square root of the product of the two numbers. Mathematically, it means that \( \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} \).

Apply the Property

Applying this property, the given expression becomes \( \sqrt{5} \cdot \sqrt{15} = \sqrt{5 \cdot 15} \).

Compute the Product

Multiply the numbers under the square root, resulting in \( \sqrt{75} \).

Simplify the Square Root

The square root of \( 75 \) can be simplified as \( 5 \sqrt{3} \). This is because \( 75 = 25 * 3 \), and \( \sqrt{25} \) equals \( 5 \). Therefore, the square root of 75 simplifies to \( 5 \sqrt{3} \).