Question

1. $-3sqrt{192}$
2. $6sqrt{96}$

Explanation:

Problem 38: $-3\sqrt{192}$

Step1: Factor out perfect square

$192 = 64 \times 3$, so $\sqrt{192} = \sqrt{64 \times 3}$

Step2: Simplify square root

$\sqrt{64 \times 3} = \sqrt{64} \times \sqrt{3} = 8\sqrt{3}$

Step3: Multiply by coefficient

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

Problem 40: $6\sqrt{96}$

Step1: Factor out perfect square

$96 = 16 \times 6$, so $\sqrt{96} = \sqrt{16 \times 6}$

Step2: Simplify square root

$\sqrt{16 \times 6} = \sqrt{16} \times \sqrt{6} = 4\sqrt{6}$

Step3: Multiply by coefficient

$6 \times 4\sqrt{6} = 24\sqrt{6}$

Answer:

1. $-24\sqrt{3}$
2. $24\sqrt{6}$