Question

Help is appreciated! Thanks!

Answer 1

Answer:

1. 16√3
2. -45+15i
3. √255
4. 6√2 +3√10

Step-by-step explanation:

1)

$-4i\sqrt{-48}=-4i\sqrt{(-1)(4^2)(3)}=(-4i)(4i)\sqrt{3}=16\sqrt{3}$

__

2)

$(-5-5i)(3-6i)=-5(3-6i)-5i(3-6i)=-15+30i-15i+30i^2=-15-30+15i\\\\=-45+15i$

__

3)

$\sqrt{3}\sqrt{5}\sqrt{17}=\sqrt{3\cdot 5\cdot 17}=\sqrt{255}$

__

4)

$\sqrt{3}(\sqrt{24}+\sqrt{30})=\sqrt{3\cdot 24}+\sqrt{3\cdot 30}=\sqrt{6^2\cdot 2}+\sqrt{3^2\cdot 10}\\\\=6\sqrt{2}+3\sqrt{10}$

_____

The applicable identities are ...

$\sqrt{a^2b}=a\sqrt{b}\\\\i^2=-1$

Answer 2

Answer:

4) $6\sqrt{2} + 3\sqrt{10}$

3) $\sqrt{255}$

2) $15i - 45$

1) $16\sqrt{3}$

Step-by-step explanation:

4) $\sqrt{3}[\sqrt{24} + \sqrt{30}] = \sqrt{72} + \sqrt{90} = \sqrt{[2][36]} + \sqrt{[10][9]} = 6\sqrt{2} + 3\sqrt{10}$

3) $\sqrt{255} = [\sqrt{3}][\sqrt{5}][\sqrt{17}]$

2) $[-5 - 5i][3 - 6i] = -15 + 15i + 30{i}^{2} = -15 + 15i - 30 = 15i - 45$

1) $-4i\sqrt{-48} = -4i\sqrt{[3][16][i]} = -4i[4i]\sqrt{3} = -16{i}^{2} \sqrt{3} = 16\sqrt{3}$

Extended Information on the Complex Number System

$\sqrt{-1} = i$

$-1 = {i}^{2}$

$-i = {i}^{3}$

$1 = {i}^{4}$

I am joyous to assist you anytime.