Question

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

Answer 1

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 2

answer : Option A

$\sqrt{-108} - \sqrt{-3}$

first we simplify each square root

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

$\sqrt{-108} =\sqrt{-36* 3}= 6i\sqrt{3}$

$\sqrt{-3} = i\sqrt{3}$ (we cannot simplify square root (3))

$\sqrt{-108} - \sqrt{-3}$

$6i\sqrt{3} - i\sqrt{3}$

Both are like terms, so we subtract it

$5i\sqrt{3}$

$5\sqrt{3} i$