Question

1. $-8sqrt{6} cdot sqrt{21}$
2. $sqrt{5}$

Explanation:

Step1: Combine square roots

$\sqrt{6} \cdot \sqrt{21} = \sqrt{6 \times 21}$

Step2: Calculate product inside root

$\sqrt{6 \times 21} = \sqrt{126}$

Step3: Simplify the square root

$\sqrt{126} = \sqrt{9 \times 14} = 3\sqrt{14}$

Step4: Multiply by the coefficient

$-8 \times 3\sqrt{14} = -24\sqrt{14}$

Answer:

$-24\sqrt{14}$