Question

simplify.
\sqrt{6} \cdot \sqrt{8}

Explanation:

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

$\sqrt{6} \cdot \sqrt{8} = \sqrt{6 \times 8}$

Step2: Calculate the product inside the square root

$6 \times 8 = 48$, so we have $\sqrt{48}$

Step3: Simplify $\sqrt{48}$ by factoring 48 into a perfect square and another number

$48 = 16 \times 3$, so $\sqrt{48} = \sqrt{16 \times 3}$

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

$\sqrt{16 \times 3} = \sqrt{16} \cdot \sqrt{3}$

Step5: Calculate $\sqrt{16}$

$\sqrt{16} = 4$, so we get $4\sqrt{3}$

Answer:

$4\sqrt{3}$