Chapter 10 Review Algebra

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). Formula: a² + b² = c².

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 a radical expression?

Back

To simplify a radical expression, factor the number under the radical into its prime factors and look for pairs of factors. For example, √18 = √(9*2) = 3√2.

Front

What does it mean to rationalize the denominator?

Back

Rationalizing the denominator means to eliminate any radicals from the denominator of a fraction. This is done by multiplying the numerator and denominator by a suitable radical.

Front

What is the difference between a rational and an irrational number?

Back

A rational number can be expressed as a fraction of two integers, while an irrational number cannot be expressed as a simple fraction. Examples: 1/2 is rational; √2 is irrational.

Front

What is the square root of 36?

Back

The square root of 36 is 6, since 6 x 6 = 36.

Front

What is the rule for adding radicals?

Back

You can only add radicals if they have the same index and radicand. For example, √2 + √2 = 2√2, but √2 + √3 cannot be simplified further.

Front

What is a right triangle?

Back

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

Front

What is the hypotenuse of a right triangle?

Back

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

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is given by the formula: Area = 1/2 * base * height.