Estimating Irrational Numbers

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers. Its decimal representation goes on forever without repeating.

Front

What is the square root of a number?

Back

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

Front

How do you estimate the square root of a number?

Back

To estimate the square root of a number, find two consecutive integers between which the number lies. For example, to estimate √20, note that 4² = 16 and 5² = 25, so √20 is between 4 and 5.

Front

Between which two integers is the square root of 44?

Back

6 and 7

Front

Between which two integers is the square root of 77?

Back

8 and 9

Front

Point B could represent which of the following numbers: √24, √30, √35, √42?

Back

√35

Front

What is the best estimate for √15?

Back

3.9

Front

Between which two whole numbers is the square root of 20?

Back

4 and 5

Front

What is the approximate value of √10?

Back

About 3.2, since 3² = 9 and 4² = 16.

Front

What is the relationship between perfect squares and their square roots?

Back

Perfect squares are numbers that are the square of an integer. Their square roots are whole numbers. For example, 16 is a perfect square, and its square root is 4.