Question

simplifying radical expressions and applying the pythagorean theorem, and solving right triangles pretest

find (x). write your answer in the form sqrt(__) with no spaces.
(x = )

Explanation:

🆕 New Concept Discovered: Pythagorean Theorem
Relating the sides of a right triangle

Step 1: Identify the sides of the right triangle

In a right-angled triangle, the side opposite the right angle is the hypotenuse (\(c\)), and the other two sides are the legs (\(a\) and \(b\)).

• Leg \(a = 8\)
• Leg \(b = x\)
• Hypotenuse \(c = \sqrt{82}\)

Step 2: Apply the Pythagorean theorem

The Pythagorean theorem states:

$$ a^2 + b^2 = c^2 $$

Substitute the known values into the equation:

$$ 8^2 + x^2 = (\sqrt{82})^2 $$

Step 3: Solve for \(x\)

Simplify the squared terms:

$$ 64 + x^2 = 82 $$

Subtract \(64\) from both sides:

$$ x^2 = 82 - 64 $$

$$ x^2 = 18 $$

Take the square root of both sides:

$$ x = \sqrt{18} $$

The problem asks for the answer in the form sqrt(_) with no spaces.

Answer:

sqrt(18)