Question

1. $\sqrt{3} \cdot \sqrt{6}$
2. $\sqrt{2} \cdot \sqrt{5}$
3. $\sqrt{5} \cdot \sqrt{10}$
4. $\sqrt{3} \cdot \sqrt{8}$
5. $\sqrt{50} \cdot \sqrt{2}$
6. $\sqrt{8} \cdot \sqrt{12}$

Explanation:

Problem 1: $\boldsymbol{\sqrt{3} \cdot \sqrt{6}}$

Step1: Use property $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$

$\sqrt{3} \cdot \sqrt{6} = \sqrt{3 \times 6}$

Step2: Simplify the product inside the square root

$\sqrt{18} = \sqrt{9 \times 2}$

Step3: Use property $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$ again

$\sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}$

Step1: Apply $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$

$\sqrt{2} \cdot \sqrt{5} = \sqrt{2 \times 5}$

Step2: Simplify the product

$\sqrt{10}$

Step1: Use $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$

$\sqrt{5} \cdot \sqrt{10} = \sqrt{5 \times 10}$

Step2: Simplify the product

$\sqrt{50} = \sqrt{25 \times 2}$

Step3: Apply $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$

$\sqrt{25 \times 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}$

Answer:

$3\sqrt{2}$

Problem 2: $\boldsymbol{\sqrt{2} \cdot \sqrt{5}}$