Question

Which choice is equivalent to the expression below?

Ì- 20
A. -20i
B. 2i Ì5
C. -2 Ì5
D. 2 Ì5i
E. 20i

Answer 1

It seems you tried to write √(-20)

use the fact tha -1 = i^2

Then, √(-20) = √(20i^2) =(√20) i = (√(5*4))i = 2√5 i = 2i√5, which seems to be what you tried to write in the option B.

Answer 2

The correct answer is D. 2i√5

Explanation:

The expression is given to be : √-20

Now, the square cannot have a negative value for any real value. So, the given expression cannot be equal to any real value.

So, The given expression is equivalent to some imaginary number.

To find the equivalent imaginary expression of the given expression we first use the relation : i² = -1

`\implies √(-20) = √(20* -1)\\\\=√(20* i^2)\\\\= √(2* 2* 5* i^2)\\\\=2\cdot i√(5)`

Hence, The given expression √-20 is equivalent to 2i√5

Therefore, The correct answer is D. 2i√5