Math Snap

STEP 1

Assumptions1. We are asked to simplify the expression $\sqrt{200}$.
. We can use the property of radicals that $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$.

STEP 2

First, we need to find the prime factorization of200. This will allow us to simplify the square root.

STEP 3

The prime factorization of200 is $2^3 \times5^2$.

STEP 4

We can rewrite $\sqrt{200}$ as $\sqrt{2^3 \times^2}$.

STEP 5

Using the property of radicals, we can rewrite this as $\sqrt{2^3} \times \sqrt{5^2}$.

STEP 6

implify $\sqrt{2^3}$ and $\sqrt{5^2}$.
$$\sqrt{2^3} =2 \sqrt{2}$$$$\sqrt{5^2} =5$$

STEP 7

Multiply the results together to get the simplified form of $\sqrt{200}$.
$$\sqrt{200} =2 \sqrt{2} \times5$$

implify the expression.
$$\sqrt{200} =10 \sqrt{2}$$Therefore, the expression $\sqrt{200}$ is equivalent to $10 \sqrt{2}$, which corresponds to option B.