Pythagorean Theorem (& Simplify 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: c² = a² + b².

Front

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

Back

The Pythagorean Theorem can only be used with right triangles.

Front

What is a radical in mathematics?

Back

A radical is a symbol that represents the root of a number, most commonly the square root. For example, √4 = 2.

Front

How do you simplify the radical √(a*b)?

Back

To simplify √(a*b), you can separate it into √a * √b, provided that both a and b are non-negative.

Front

What is the simplified form of √(36)?

Back

The simplified form of √(36) is 6.

Front

What is the approximate value of √(50)?

Back

The approximate value of √(50) is about 7.07.

Front

How do you simplify the expression 2√(8)?

Back

2√(8) can be simplified to 4√(2) because √(8) = √(4*2) = 2√(2).

Front

What is the value of x in the equation 3² + 4² = x²?

Back

Using the Pythagorean Theorem, x² = 3² + 4² = 9 + 16 = 25, so x = 5.

Front

What is the simplified form of √(12)?

Back

The simplified form of √(12) is 2√(3).

Front

How do you find the hypotenuse of a right triangle with legs of length 5 and 12?

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169, so c = √(169) = 13.