Answer:
[tex]\sqrt{-25} = 5i[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{-25[/tex]
Required
An equivalent
We have:
[tex]\sqrt{-25[/tex]
Express -25 as -1 * 25
[tex]\sqrt{-25} = \sqrt{-1 * 25}[/tex]
Split
[tex]\sqrt{-25} = \sqrt{-1} * \sqrt{25}[/tex]
[tex]\sqrt{25} = 5[/tex], so:
[tex]\sqrt{-25} = \sqrt{-1} * 5[/tex]
[tex]\sqrt{-1} = i[/tex] --- complex numbers
So:
[tex]\sqrt{-25} = i * 5[/tex]
[tex]\sqrt{-25} = 5i[/tex]
Hence, the equivalent is (D)
