Week 22 Flashcard Algebra 1 Radicals

Front

What is a radical in mathematics?

Back

A radical is a symbol used to indicate the root of a number, most commonly the square root. It is represented by the radical sign (√).

Front

How do you simplify a square root?

Back

To simplify a square root, 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 number.

Front

What is the square root of 16?

Back

The square root of 16 is 4, since 4 x 4 = 16.

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 (e.g., 1, 4, 9, 16). A non-perfect square cannot be expressed as such (e.g., 2, 3, 5).

Front

How do you add or subtract radicals?

Back

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

Front

What is the product of two radicals?

Back

The product of two radicals can be simplified by multiplying the numbers under the radicals together. For example, √a * √b = √(a*b).

Front

What is the quotient of two radicals?

Back

The quotient of two radicals can be simplified by dividing the numbers under the radicals. For example, √a / √b = √(a/b), provided b is not zero.

Front

What is the radical form of 27?

Back

The radical form of 27 is √(27), which can be simplified to 3√3.

Front

How do you rationalize the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by a radical that will eliminate the radical in the denominator. For example, to rationalize 1/√2, multiply by √2/√2 to get √2/2.

Front

What is the relationship between exponents and radicals?

Back

Radicals can be expressed in terms of exponents. For example, √a can be written as a^(1/2) and the nth root of a as a^(1/n).