Question

Remove all perfect squares from inside the square root assume y is positive ✔️200y^4

Answer 1

$\bf \sqrt{200y^4}\qquad \begin{cases} 200=2\cdot 2\cdot 2\cdot 5\cdot 5\\ \qquad 2^2\cdot 2\cdot 5^2\\ y^4=y^{2+2}\\ \qquad y^2\cdot y^2\\ \qquad (y^2)^2 \end{cases}\implies \sqrt[2]{2^2\cdot 2\cdot 5^2\cdot (y^2)^2} \\\\\\ 2\cdot 5\cdot y^2\sqrt{2}\implies 10y^2\sqrt{2}$