Simplify Radicals and Pythagorean Theorem

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.

Front

How do you simplify √a * √b?

Back

√a * √b = √(a * b) for non-negative a and b.

Front

What is the Pythagorean Theorem?

Back

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

Simplify √200.

Back

10√2.

Front

What is the first step in simplifying a radical?

Back

Factor the number under the radical into its prime factors.

Front

How do you simplify √128?

Back

√128 = √(64 * 2) = √64 * √2 = 8√2.

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.

Front

Find the measure of the missing side if one side is 4 and the other is 3 using the Pythagorean Theorem.

Back

The missing side is 5 (√(4² + 3²) = √(16 + 9) = √25 = 5).

Front

Solve for x: x² = 72.

Back

x = 6√2.

Front

What is the simplified form of √(a²)?

Back

The simplified form is |a|.