8-1 & Radicals Review

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

How do you classify a triangle based on its angles?

Back

Triangles can be classified as: 1. Acute Triangle: All angles are less than 90 degrees. 2. Right Triangle: One angle is exactly 90 degrees. 3. Obtuse Triangle: One angle is greater than 90 degrees.

Front

What is a right triangle?

Back

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

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): c² = a² + b².

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

How do you simplify a square root?

Back

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

Front

What is the value of √(a²)?

Back

The value of √(a²) is |a|, which means the absolute value of a.

Front

How do you add or subtract radicals?

Back

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

Front

What is the process to multiply two radicals?

Back

To multiply two radicals, multiply the numbers inside the radicals and then simplify if possible. For example, √2 * √3 = √(2*3) = √6.

Front

What is the value of x if x² = 81?

Back

x = ±9.