[tex]\sqrt{a}=b\iff b^2=a\\\\\text{for}\ a\geq0\ \text{and}\ b\geq0[/tex]
[tex]\text{If is}\ \sqrt{200\cdot2},\ \text{then}\\\\\sqrt{200\cdot2}=\sqrt{400}=20\ \text{because}\ 20^2=400[/tex]
[tex]\text{If is}\ \sqrt{200}\cdot2,\ \text{then}\\\\\sqrt{200}\cdot2=2\sqrt{200}=2\sqrt{100\cdot2}=2\cdot\sqrt{100}\cdot\sqrt2=2\cdot10\cdot\sqrt2=20\sqrt2\\\\\text{If you want approximation, then}\ \sqrt2\approx1.41,\\\\ \text{therefore}\ 20\sqrt2\approx20\cdot1.41=28.2\\\\\sqrt{100}=10\ \text{because}\ 10^2=100\\\\\text{used}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\ \text{for}\ a\geq0\ \text{and}\ b\geq0.[/tex]
