Question

Which expression is equivalent to square root of -80

Answer 1

Answer:

The equivalent expression is $(4\sqrt{5})i$

Step-by-step explanation:

Given the expression $\sqrt{-80}$ we can use prime factorization and a property of imaginary numbers to obtain an equivalent expression.

Let's start applying prime factorization over $80$

$80=(2).(40)=(2).(2).(20)=(2).(2).(2).(10)=(2).(2).(2).(2).(5)=(2^{4}).(5)$

The other property is $i^{2}=-1$ (This is a property of imaginary numbers).

We can write $-80$ as

$-80=(2^{4}).(5).i^{2}$

Now we apply square root to the expression ⇒

$\sqrt{(2^{4}).(5).i^{2}}=(4\sqrt{5})i$

Answer 2

Sqrt(-80) = 8.94427191i
Hope it helped :d