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 can you estimate the square root of a number?

Back

To estimate the square root of a number, find the two perfect squares it lies between and then determine a value between those two integers.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

Front

What are the perfect squares between 1 and 100?

Back

The perfect squares between 1 and 100 are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Front

What is the approximate value of the square root of 80?

Back

The approximate value of the square root of 80 is about 8.9.

Front

Which two integers does the square root of 44 lie between?

Back

The square root of 44 lies between the integers 6 and 7.

Front

Which two integers does the square root of 77 lie between?

Back

The square root of 77 lies between the integers 8 and 9.

Front

How do you determine if a number is a perfect square?

Back

To determine if a number is a perfect square, find its square root and check if the result is an integer.

Front

What is the square root of 225?

Back

The square root of 225 is 15, making it a perfect square.