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:
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.