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The image shows a right triangle where one leg is labeled \( \sqrt{55} \), the other leg is labeled \( 8 \), and we are asked to find the length of the third side (the hypotenuse) in simplest radical form.

To solve this, we can use the **Pythagorean Theorem**:
\[
c^2 = a^2 + b^2
\]
where \( c \) is the hypotenuse, and \( a \) and \( b \) are the legs of the right triangle.

Given:
- \( a = \sqrt{55} \)
- \( b = 8 \)

Substitute into the formula:
\[
c^2 = (\sqrt{55})^2 + 8^2
\]
\[
c^2 = 55 + 64
\]
\[
c^2 = 119
\]

Now take the square root of both sides:
\[
c = \sqrt{119}
\]

Thus, the length of the hypotenuse is \( \sqrt{119} \), which is already in its simplest radical form.

Would you like further clarification or details on this problem? Here are some related questions for further practice:

1. What if both legs of a right triangle are known, and you need to find the hypotenuse?
2. How do you determine if a radical expression is in its simplest form?
3. Can you simplify \( \sqrt{119} \) further if it were not prime?
4. How does the Pythagorean Theorem apply to non-right triangles?
5. What is the difference between an exact solution in radical form versus a decimal approximation?

**Tip:** When solving for the hypotenuse, always verify that the radical form is simplified by checking for perfect square factors in the radicand.

Find the length of the third side. If necessary, write in simplest radical form. (A right triangle with one leg labeled as \( \sqrt{55} \) and the other as \( 8 \))

Learn how to find the length of the hypotenuse in a right triangle using the Pythagorean Theorem. This example involves one leg labeled as \( \sqrt{55} \) and the other as 8, with the solution provided in simplest radical form. Suitable for students in Grades 8-10.

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