Real numbers on the number line/irrational numbers

Front

What is a real number?

Back

A real number is any number that can be found on the number line, including both rational and irrational numbers.

Front

Define irrational numbers.

Back

Irrational numbers are numbers that cannot be expressed as a fraction of two integers. Their decimal representation is non-repeating and non-terminating.

Front

What is the square root of a number?

Back

The square root of a number x is a value that, when multiplied by itself, gives x. For example, √9 = 3.

Front

How do you approximate the square root of a non-perfect square?

Back

To approximate the square root of a non-perfect square, find two perfect squares it lies between and estimate its value based on their square roots.

Front

What is the area of a square?

Back

The area of a square is calculated by squaring the length of one of its sides (Area = side²).

Front

If the area of a square is 100 square feet, what is the length of one side?

Back

The length of one side is √100 = 10 feet.

Front

What is the relationship between the area of a square and its side length?

Back

The area of a square increases with the square of its side length; doubling the side length increases the area by a factor of four.

Front

What is the value of √8?

Back

√8 is approximately 2.83, which is an irrational number.

Front

How can you express 7/3.5 as a decimal?

Back

7/3.5 = 2, which is a rational number.

Front

What is π (pi)?

Back

π is an irrational number approximately equal to 3.14, representing the ratio of the circumference of a circle to its diameter.