Question

which expression is equivalent to square root of -80? A) -4 square root 5 B) -4 square root 5i C)4 square root 5i D) 4 square root 5

Answer 1

C) 4 square root 5i............

Answer 2

Option (C) is correct.

an equivalent expression for the given expression square root of -80 is
`4+√(5)i`

Explanation:

Given: square root of -80

We have to find an equivalent expression.

Consider the given expression square root of -80

This can be written mathematically as
`√(-80)`

Since, prime factorization of 80 is 2 × 2 × 2 ×2 × 5

Thus,
`√(-80)=√(-2* 2* 2 * 2*5)`

Simplify , we get,

`√(-2* 2*2* 2 *5)=4√(-5)`

Also,
`√(-1)=i`

Thus,
`4√(-5)=4+√(5)i`

Thus, an equivalent expression for the given expression square root of -80 is
`4+√(5)i`

Option (C) is correct.