Question

What’s the square root of 200 times 2

Answer 1

The square root of 200 is roughly 14.14, and that times 2 is 28.28, but if you were looking for the square root of “200 times 2” (all of that under a square root) then its the sq root of 400 (2*200), which is 20.

Answer 2

`√(a)=b\iff b^2=a\\\\\text{for}\ a\geq0\ \text{and}\ b\geq0`

`\text{If is}\ √(200\cdot2),\ \text{then}\\\\√(200\cdot2)=√(400)=20\ \text{because}\ 20^2=400`

`\text{If is}\ √(200)\cdot2,\ \text{then}\\\\√(200)\cdot2=2√(200)=2√(100\cdot2)=2\cdot√(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\\\\√(100)=10\ \text{because}\ 10^2=100\\\\\text{used}\ √(a\cdot b)=√(a)\cdot√(b)\ \text{for}\ a\geq0\ \text{and}\ b\geq0.`