Answer: Solve : x2+64 = 0
Subtract 64 from both sides of the equation :
x2 = -64
When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:
x = ± √ -64
In Math, i is called the imaginary unit. It satisfies i2 =-1. Both i and -i are the square roots of -1
Accordingly, √ -64 =
√ -1• 64 =
√ -1 •√ 64 =
i • √ 64
Can √ 64 be simplified ?
Yes! The prime factorization of 64 is
2•2•2•2•2•2
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).
√ 64 = √ 2•2•2•2•2•2 =2•2•2•√ 1 =
± 8 • √ 1 =
± 8
