Question

Find the square rots of −5. Show that the square rots satisfy the equation x2 + 5 = 0.

Answer 1

Answer:

The root of -5 is +√5i and -√5i.

Step-by-step explanation:

Given data in the question is -5.

To find:-

Square roots of -5.

Solution:-

⇒±√-5

⇒±√5*√-1

⇒±√5i        (√-1=i(iota)

Given Equation

$x^2+5=0\\x^2=-5\\x=\sqrt{-5}$ and $x=-\sqrt{-5} \\x=\sqrt{5}*\sqrt{-1}\\ x=\sqrt{5}i$ and $x=-\sqrt{5}i$

Answer 2

Answer:

The square roots satisfies the equation

Step-by-step explanation:

$\sqrt{-5}=\sqrt{5\times -1}\\ =\sqrt{5}\times \sqrt{-1}\\ =2.23606i$

As the square root of negative 1 is not real it is denoted by

$\sqrt{-1}=i$

In the given equation

$x^2+5=0\\\Rightarrow x^2=-5\\\Rightarrow x=\sqrt{-5}\\\Rightarrow x=\sqrt{5\times -1}\\\Rightarrow x=\sqrt{5}\times \sqrt{-1}\\\Rightarrow x=2.23606i$

So, the square roots satisfies the equation.