Pythagorean Theorem and Simplifying 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 are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if one of its angles measures 90 degrees. Additionally, it must satisfy the Pythagorean Theorem: a² + b² = c².

Front

How do you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.

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 represents the square root of 4.

Front

How do you simplify a radical?

Back

To simplify a radical, factor the number under the radical into its prime factors, and then pair the factors. Each pair can be taken out of the radical as a single number.

Front

What is the simplified form of √24?

Back

The simplified form of √24 is 2√6.

Front

What is the simplified form of √300?

Back

The simplified form of √300 is 10√3.

Front

What does it mean to simplify a radical completely?

Back

To simplify a radical completely means to express it in its simplest form, where no perfect square factors remain under the radical.

Front

What is the value of x in the equation x² = 16?

Back

The value of x is 4, since √16 = 4.

Front

What is the relationship between the sides of a 3-4-5 triangle?

Back

In a 3-4-5 triangle, the lengths of the sides satisfy the Pythagorean Theorem: 3² + 4² = 5².