Pythagorean Review

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

How do you simplify a radical expression?

Back

To simplify a radical expression, 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 factor.

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

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

How do you find the length of an unknown side in a right triangle?

Back

To find the length of an unknown side in a right triangle, you can use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. It is denoted as √x.

Front

What does it mean to 'simplify' a radical?

Back

To 'simplify' a radical means to express it in its simplest form, removing any perfect square factors from under the radical.

Front

What is the value of √19?

Back

√19 is an irrational number approximately equal to 4.36.

Front

What is the value of 6√2?

Back

6√2 is an expression that represents approximately 8.49, as √2 is approximately 1.41.

Front

How do you calculate the length of the hypotenuse if the other two sides are known?

Back

To calculate the length of the hypotenuse, use the formula c = √(a² + b²), where a and b are the lengths of the other two sides.