Question

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

Answer 1

The root of -5 is +√5i and -√5i.

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=√(-5) \\` and
`x=-√(-5) \\x=√(5)*√(-1)\\ x=√(5)i` and
`x=-√(5)i`

Answer 2

The square roots satisfies the equation

Explanation:

`√(-5)=√(5* -1)\\ =√(5)* √(-1)\\ =2.23606i`

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

`√(-1)=i`

In the given equation

`x^2+5=0\\\Rightarrow x^2=-5\\\Rightarrow x=√(-5)\\\Rightarrow x=√(5* -1)\\\Rightarrow x=√(5)* √(-1)\\\Rightarrow x=2.23606i`

So, the square roots satisfies the equation.