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

Answer:

Option (C) is correct.

an equivalent expression for the given expression  square root of -80 is $4+\sqrt{5}i$

Step-by-step 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 $\sqrt{-80}$

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

Thus, $\sqrt{-80}=\sqrt{-2\times 2\times 2 \times 2\times5}$

Simplify , we get,

$\sqrt{-2\times 2\times2\times 2 \times5}=4\sqrt{-5}$

Also, $\sqrt{-1}=i$

Thus, $4\sqrt{-5}=4+\sqrt{5}i$

Thus, an equivalent expression for the given expression  square root of -80 is $4+\sqrt{5}i$

Option (C) is correct.