Algebra - Ch 10 - Pythagorean Theorem & Radicals

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

What type of triangle can the Pythagorean Theorem be applied to?

Back

The Pythagorean Theorem can only be used with right triangles.

Front

Simplify: √(16)

Back

4

Front

Solve for x: x² = 32. What is x in simplest radical form?

Back

x = 4√2

Front

What is a radical?

Back

A radical is a symbol (√) that represents the root of a number, most commonly the square root.

Front

Simplify: √(50)

Back

5√2

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

5 (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the square root of 81?

Back

9

Front

Solve for x: x² = 18. What is x in simplest radical form?

Back

x = 3√2