contestada

Which expression is equivalent to sqrt -108 - sqrt -3

A) 5 sqrt 3i
B) 6 sqrt 3i
C) 7 sqrt 3i
D) 8 sqrt 3i

Which expression is equivalent to sqrt 108 sqrt 3 A 5 sqrt 3i B 6 sqrt 3i C 7 sqrt 3i D 8 sqrt 3i class=

Respuesta :

sqrt (-108) - sqrt (-3)

sqrt(-1) sqrt(108) - sqrt(-1) sqrt(3)

sqrt(-1)*sqrt(36)*sqrt(3)-sqrt(-1)sqrt(3)

sqrt(-1)sqrt(3) (6-1)

isqrt(3)5

5isqrt(3)

Choice A


answer : Option A

[tex]\sqrt{-108} - \sqrt{-3}[/tex]

first we simplify each square root

The value of square root (-1) = i, to remove negative inside the square root we use 'i'

[tex]\sqrt{-108} =\sqrt{-36* 3}= 6i\sqrt{3} [/tex]

[tex]\sqrt{-3} = i\sqrt{3} [/tex] (we cannot simplify square root (3))

[tex]\sqrt{-108} - \sqrt{-3}[/tex]

[tex]6i\sqrt{3} - i\sqrt{3}[/tex]

Both are like terms, so we subtract it

[tex]5i\sqrt{3}[/tex]

[tex]5\sqrt{3} i [/tex]

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