Question

simplify.
\sqrt{15} \cdot \sqrt{5}

Explanation:

Step1: Use property of square roots ($\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$)

$\sqrt{15} \cdot \sqrt{5} = \sqrt{15 \times 5}$

Step2: Calculate the product inside the square root

$\sqrt{15 \times 5} = \sqrt{75}$

Step3: Simplify $\sqrt{75}$ by factoring 75

$\sqrt{75} = \sqrt{25 \times 3}$

Step4: Use property of square roots again ($\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$)

$\sqrt{25 \times 3} = \sqrt{25} \cdot \sqrt{3}$

Step5: Simplify $\sqrt{25}$

$\sqrt{25} \cdot \sqrt{3} = 5\sqrt{3}$

Answer:

$5\sqrt{3}$