Answer:
[tex]\large\boxed{\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot\sqrt{y^2}\cdot\sqrt{y}}\\\boxed{2\cdot2\cdot y\sqrt{2\cdot5\cdot7\cdot y}}\\\boxed{4y\sqrt{70y}}[/tex]
Step-by-step explanation:
[tex]\begin{array}{c|c}1120&2\\560&2\\280&2\\140&2\\70&2\\35&5\\7&7\\1\end{array}\\\\1,120=2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot7=2^2\cdot2^2\cdot2^2\cdot2\cdot5\cdot7\\\\y^3=y\cdot y\cdot y=y^2\cdot y[/tex]
[tex]\sqrt{1,120y^3}=\sqrt{2^2\cdot2^2\cdot2\cdot5\cdot7\cdot y^2\cdot y}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot\sqrt{y^2}\cdot\sqrt{y}\\\\\sqrt{1,120y^3}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{y^2}\cdot\sqrt{2\cdot5\cdot7\cdot y}\qquad\text{use}\ \sqrt{a^2}=a\\\\=2\cdot2\cdot y\cdot\sqrt{2\cdot5\cdot7\cdot y}\\\\\sqrt{1,120y^3}=2\cdot2\cdot y\cdot\sqrt{2\cdot5\cdot7\cdot y}=4y\sqrt{70y}[/tex]
