which radical is represented in the following figu

Question

Accepted Answer

# Explanation:
## Step1: Use the Pythagorean theorem
The Pythagorean theorem states that in a right - triangle $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs of the right - triangle. In the right - triangle with one leg $AB = 2$ (distance from $A(0)$ to $B(2)$) and the other leg $BC = 1$.
Let the hypotenuse be $AC$. Then $AC^{2}=AB^{2}+BC^{2}$. Substituting $AB = 2$ and $BC = 1$, we get $AC^{2}=2^{2}+1^{2}$.
## Step2: Calculate the value of $AC$
$$
\begin{align*}
AC^{2}&=4 + 1\
AC^{2}&=5\
AC&=\sqrt{5}
\end{align*}
$$

# Answer:
$\sqrt{5}$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the Pythagorean theorem

Step2: Calculate the value of \(AC\)

Answer: