Question

Can someone please help me

Answer 1

`\large\boxed{√(2^2)\cdot√(2^2)\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot√(y^2)\cdot√(y)}\\\boxed{2\cdot2\cdot y√(2\cdot5\cdot7\cdot y)}\\\boxed{4y√(70y)}`

Explanation:

`\begin{array}c1120&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`

`√(1,120y^3)=√(2^2\cdot2^2\cdot2\cdot5\cdot7\cdot y^2\cdot y)\qquad\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=√(2^2)\cdot√(2^2)\cdot\sqrt2\cdot\sqrt5\cdot\sqrt7\cdot√(y^2)\cdot√(y)\\\\√(1,120y^3)=√(2^2)\cdot√(2^2)\cdot√(y^2)\cdot√(2\cdot5\cdot7\cdot y)\qquad\text{use}\ √(a^2)=a\\\\=2\cdot2\cdot y\cdot√(2\cdot5\cdot7\cdot y)\\\\√(1,120y^3)=2\cdot2\cdot y\cdot√(2\cdot5\cdot7\cdot y)=4y√(70y)`