Nicky156
contestada

Help is appreciated! Thanks!
I really need these answers explained!!

1) Simplify
-4i√-48

2) Multiply. Give your answer in radical form. (-5-5i)(3-6i)

3) Multiply. Give your answer in radical form. √3√5√17

4) Multiply. Give your answer in radical form. √3(√24+√30)

Respuesta :

sqdancefan

Answer:

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

Step-by-step explanation:

1)

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

__

2)

[tex](-5-5i)(3-6i)=-5(3-6i)-5i(3-6i)=-15+30i-15i+30i^2=-15-30+15i\\\\=-45+15i[/tex]

__

3)

[tex]\sqrt{3}\sqrt{5}\sqrt{17}=\sqrt{3\cdot 5\cdot 17}=\sqrt{255}[/tex]

__

4)

[tex]\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}[/tex]

_____

The applicable identities are ...

[tex]\sqrt{a^2b}=a\sqrt{b}\\\\i^2=-1[/tex]

BasketballEinstein

Answer:

4) [tex]6\sqrt{2} + 3\sqrt{10}[/tex]

3) [tex]\sqrt{255}[/tex]

2) [tex]15i - 45[/tex]

1) [tex]16\sqrt{3}[/tex]

Step-by-step explanation:

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

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

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

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

Extended Information on the Complex Number System

[tex]\sqrt{-1} = i[/tex]

[tex]-1 = {i}^{2}[/tex]

[tex]-i = {i}^{3}[/tex]

[tex]1 = {i}^{4}[/tex]

I am joyous to assist you anytime.

Otras preguntas