Approximate Irrational Numbers

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a fraction of two integers. Its decimal representation is non-repeating and non-terminating.

Front

What is the approximate value of √98?

Back

√98 is approximately 9.899, which lies between 9 and 10 on the number line.

Front

Identify a rational number from the following: √20, √64, 6π, √7.

Back

√64 is a rational number because it equals 8, which can be expressed as a fraction (8/1).

Front

What is the approximate value of √7?

Back

√7 is approximately 2.646, which is an irrational number.

Front

Between which two integers does √77 lie?

Back

√77 is approximately 8.775, which lies between 8 and 9.

Front

What is the approximate value of √40?

Back

√40 is approximately 6.325, which lies between 6 and 7.

Front

How can you determine if a square root is rational or irrational?

Back

A square root is rational if it is the square of a whole number. If it is not, it is irrational.

Front

What is the decimal representation of an irrational number?

Back

The decimal representation of an irrational number is non-repeating and non-terminating.

Front

Give an example of an irrational number.

Back

An example of an irrational number is π (pi), which is approximately 3.14159.

Front

What is the significance of the number line in understanding irrational numbers?

Back

The number line helps visualize where irrational numbers fall between rational numbers, showing their density.