Simplifying radicals

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

What does it mean to simplify a radical?

Back

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

Front

What is the square root of 16?

Back

The square root of 16 is 4.

Front

How do you simplify √50?

Back

√50 can be simplified to 5√2 because 50 = 25 * 2, and √25 = 5.

Front

What is the difference between a perfect square and a non-perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer, while a non-perfect square cannot.

Front

What is the square root of 25?

Back

The square root of 25 is 5.

Front

How do you simplify √72?

Back

√72 can be simplified to 6√2 because 72 = 36 * 2, and √36 = 6.

Front

What is the product property of square roots?

Back

The product property states that √a * √b = √(a*b) for any non-negative numbers a and b.

Front

What is the quotient property of square roots?

Back

The quotient property states that √(a/b) = √a / √b for any non-negative numbers a and b, where b ≠ 0.

Front

How do you add or subtract radicals?

Back

You can only add or subtract radicals if they have the same index and radicand (the number under the radical). For example, √2 + √2 = 2√2, but √2 + √3 cannot be simplified further.