which expression is equivalent to $sqrt{200}$?\n$2sqrt{10}$\n$10sqrt{2}$\n$10sqrt{20}$\n$100sqrt{2}$
which expression is equivalent to $sqrt{200}$?\n$2sqrt{10}$\n$10sqrt{2}$\n$10sqrt{20}$\n$100sqrt{2}$
Answer
Explanation:
Step1: Prime - factorize 200
$200 = 2\times100=2\times10\times10$
Step2: Simplify the square - root
$\sqrt{200}=\sqrt{10\times10\times2}$ Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a = 10\times10$, $b = 2$), we get $\sqrt{10\times10}\cdot\sqrt{2}=10\sqrt{2}$
Answer:
10$\sqrt{2}$ (corresponding to the second option)