The problem asks to find the radius of a circle given its equation $(x + 2)^2 + y^2 = 20$.

1. Problem Description

The problem asks to find the radius of a circle given its equation $(x + 2)^2 + y^2 = 20$.

2. Solution Steps

The general equation of a circle with center $(h, k)$ and radius $r$ is given by:

$(x - h)^2 + (y - k)^2 = r^2$

Comparing the given equation $(x + 2)^2 + y^2 = 20$ with the general equation, we can rewrite the given equation as:

$(x - (-2))^2 + (y - 0)^2 = 20$

Here, the center of the circle is $(-2, 0)$.

We have $r^2 = 20$.

To find the radius $r$, we take the square root of both sides:

$r = \sqrt{20}$

We can simplify the radical by factoring out the largest perfect square from

2

0. Since $20 = 4 \times 5$, we have:

$r = \sqrt{4 \times 5}$

$r = \sqrt{4} \times \sqrt{5}$

$r = 2\sqrt{5}$

3. Final Answer

The radius of the circle is $2\sqrt{5}$.