Question

multiply. write your answer in simplest form.\\(\sqrt{33} \cdot \sqrt{50}\\)

Explanation:

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

$\sqrt{33} \cdot \sqrt{50} = \sqrt{33 \times 50}$

Step2: Simplify the product inside the square root

$33 \times 50 = 1650$, so we have $\sqrt{1650}$

Step3: Factor 1650 to find perfect square factors

$1650 = 25 \times 66$, and $25$ is a perfect square. So $\sqrt{1650} = \sqrt{25 \times 66}$

Step4: Use the property $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ again

$\sqrt{25 \times 66} = \sqrt{25} \cdot \sqrt{66} = 5\sqrt{66}$

Answer:

$5\sqrt{66}$