Question

Simplify the equation and write the answer without negative exponents

Answer 1

`\bf √(200)-√(32)\quad \begin{cases} 200=2\cdot 2\cdot 2\cdot 5\cdot 5\\ \qquad 2^2\cdot 2\cdot 5^2\\ \qquad (2\cdot 5)^2\cdot 2\\ \qquad (10)^2\cdot 2\\ 32=2\cdot 2\cdot 2\cdot 2\cdot 2\\ \qquad 2^2\cdot 2^2\cdot 2\\ \qquad (2\cdot 2)^2\cdot 2\\ \qquad (4)^2\cdot 2 \end{cases}\implies √(10^2\cdot 2)-√(4^2\cdot 2) \\\\\\ 10√(2)-4√(2)\implies 6√(2)\implies 6\cdot 2^{(1)/(2)}`

Answer 2

`√(200) - √(32) = √(2 * 100) - √(2 * 16) = 10 √(2) - 4 √(2) = 6 √(2)`