Question

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

Answer 1

Answer:

x>0 and working with real numbers

$10x^2\sqrt{2}$

OR

x<0 and working with imaginary/complex numbers

$10\sqrt{2}\sqrt{x^4}$

OR

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

$10\sqrt{2}\sqrt{x^4}$

Step-by-step explanation:

$\sqrt{200x^4}$

First simplify $\sqrt{200}$

$\sqrt{200}$

Find a perfect square and a non perfect square, which when you multiply the two squares it gives you $\sqrt{200}$

$\sqrt{100} * \sqrt{2} = \sqrt{200}$

$\sqrt{100} \ \sqrt{2}}$

$10 \sqrt{2}$

Now get the square root of $\sqrt{x^4}$ if we are working with real numbers and  x > 0

$\sqrt{x^4} = x^2$

If x not > 0 then just leave as $\sqrt{x^4}$

Now combine it all

$10x^2\sqrt{2}$

OR

$10\sqrt{2}\sqrt{x^4}$