Question

Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.


`\sqrt{200x^(4 )`


What is the simplified form of the​ expression?

Answer 1

x>0 and working with real numbers

`10x^2√(2)`

OR

x<0 and working with imaginary/complex numbers

`10√(2)√(x^4)`

OR

Leave it like the following for both systems(Real/Complex) numbers

`10√(2)√(x^4)`

Explanation:

`√(200x^4)`

First simplify
`√(200)`

`√(200)`

Find a perfect square and a non perfect square, which when you multiply the two squares it gives you
`√(200)`

`√(100) * √(2) = √(200)`

`√(100) \ √(2)}`

`10 √(2)`

Now get the square root of
`√(x^4)` if we are working with real numbers and x > 0

`√(x^4) = x^2`

If x not > 0 then just leave as
`√(x^4)`

Now combine it all

`10x^2√(2)`

OR

`10√(2)√(x^4)`