Find the square rots of −5. Show that the square rots satisfy the equation x2 + 5 = 0.
Accepted Solution
A:
Answer:The square roots satisfies the equationStep-by-step explanation:[tex]\sqrt{-5}=\sqrt{5\times -1}\\ =\sqrt{5}\times \sqrt{-1}\\ =2.23606i[/tex]As the square root of negative 1 is not real it is denoted by[tex]\sqrt{-1}=i[/tex]In the given equation[tex]x^2+5=0\\\Rightarrow x^2=-5\\\Rightarrow x=\sqrt{-5}\\\Rightarrow x=\sqrt{5\times -1}\\\Rightarrow x=\sqrt{5}\times \sqrt{-1}\\\Rightarrow x=2.23606i[/tex]So, the square roots satisfies the equation.