I need help Simplifying a Term Under a Radical Sign please

[Mike llado]

√-64x⁴

 

[Mike llado]

I don't know how to solve this at all.

 

[srmichael]

I don't know how to solve this at all.

Really? You are in Intermediate/Advanced Algebra and this one is stumping you?

 

[Mike llado]

yes I am horrible at math and it doesn't help that its been a few years since I've actively done math at all

 

[pka]

√-64x⁴

There is nothing to simplify \(\displaystyle \sqrt{-64x^4}\) does not exist in the real number system.

However, using complex numbers \(\displaystyle \sqrt{-64x^4}=8ix^2.\)

 

[Mike llado]

So your saying it cant be solved? I don't understand the complex answer part

 

[pka]

So your saying it cant be solved? I don't understand the complex answer part

In the real number system there is no square roots of negative numbers.

The complex system we extend the real number system by adding the number \(\displaystyle i\) having the property that \(\displaystyle i^2=-1\)

So while \(\displaystyle \sqrt{-64}\) does not exist as a real number, as a complex number \(\displaystyle \sqrt{-64}=8i\) because \(\displaystyle (8i)^2=64i^2=-64.\)

 

[JeffM]

So your saying it cant be solved? I don't understand the complex answer part

It can be simplified. If x is a real number:

\(\displaystyle \sqrt{-64x^2} = \sqrt{64 * (-1) * x^2} = \sqrt{64} * \sqrt{-1} * \sqrt{x^2} = 8i * |x|.\)

If x is a complex number:

\(\displaystyle \sqrt{-64x^2} = \sqrt{64 * (- 1) * x^2} = \sqrt{64} * \sqrt{- 1} * \sqrt{x^2} = 8i\sqrt{x^2}.\)

However, NONE of those expressions represents a real number. They ALL represent a complex number.