Simplifying Radicals and Rational Numbers

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction; it cannot be written as a ratio of two integers.

Front

What is the result of adding a rational number to an irrational number?

Back

The result is always an irrational number.

Front

How do you simplify the expression 6√3 + 2√75 - 4√27?

Back

First, simplify each term: 2√75 = 2√(25*3) = 10√3 and 4√27 = 4√(9*3) = 12√3. Then combine like terms: 6√3 + 10√3 - 12√3 = 4√3.

Front

What is the simplified form of √200?

Back

√200 can be simplified to 10√2, since 200 = 100 * 2 and √100 = 10.

Front

What is the product of (-2√7) and (3√28)?

Back

The product is -84, since (-2√7)(3√28) = -6√(7*28) = -6√196 = -6*14 = -84.

Front

What does it mean to simplify a radical expression?

Back

To simplify a radical expression means to rewrite it in its simplest form, removing any perfect square factors from under the radical.

Front

What are perfect squares?

Back

Perfect squares are numbers that are the square of an integer, such as 1, 4, 9, 16, 25, etc.

Front

How do you determine if a number is rational or irrational?

Back

A number is rational if it can be expressed as a fraction of two integers; it is irrational if it cannot be expressed in this way.

Front

What is the square root of 28 simplified?

Back

The square root of 28 can be simplified to 2√7, since 28 = 4 * 7 and √4 = 2.