Which expression is equivalent to square root of -80

Question

asked Feb 5, 2017 108k views

2 Answers

Sblandin · Answer 1 · 2017-02-11T14:55:55+0000

Answer:

The equivalent expression is
(4√(5))i

Explanation:

Given the expression
√(-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=(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
as

-80=(2^(4)).(5).i^(2)

Now we apply square root to the expression ⇒

$\sqrt{(2^(4)).(5).i^(2)}=(4√(5))i$