Question

Simplify by factoring.
Sqrt 500x^4

is the answer sqrt10x?

Answer 1

I got \[10x^2\sqrt{5x^2}\]

Answer 2

You can factor 500 into 100*5. Notice how one of the factors is a perfect square.


So \[\sqrt{500}=\sqrt{100*5}=\sqrt{100}\sqrt{5}=10\sqrt{5}\]


which means that \[\sqrt{500}=10\sqrt{5}\]


Furthermore, \[\sqrt{x^4}=x^2\]


So altogether, \[\sqrt{500x^4}=10x^2\sqrt{5}\]

Answer 3

What about the remainder of the x?

Answer 4

Notice how \[(x^2)^2=x^{(2*2)}=x^4\], so the square root of that "undoes" \[x^4\] and reverts it back to \[x^2\]


So this means that \[\sqrt{x^4}=x^2\]