Estimating irrational numbers review

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 approximate value of √12?

Back

The approximate value of √12 is 3.5.

Front

How do you estimate the value of √7?

Back

To estimate √7, you can find two perfect squares it lies between: 2^2 (4) and 3^2 (9). Thus, √7 is between 2.5 and 2.65.

Front

What is the process for rounding √119 to the nearest tenth?

Back

To round √119 to the nearest tenth, first calculate its approximate value (which is about 10.9087) and then round it to 10.9.

Front

Define whole numbers.

Back

Whole numbers are the set of non-negative numbers that include zero and all positive integers, without any fractions or decimals.

Front

What is the best approximation of point M if it is represented as 7/3.5?

Back

The best approximation of point M is 2, since 7 divided by 3.5 equals 2.

Front

How can you estimate square roots of non-perfect squares?

Back

To estimate square roots of non-perfect squares, find the nearest perfect squares below and above the number, then interpolate between their square roots.

Front

What is the significance of estimating irrational numbers in real-life applications?

Back

Estimating irrational numbers is important in real-life applications such as engineering, physics, and finance, where precise calculations are often impractical.

Front

What is the approximate value of √2?

Back

The approximate value of √2 is about 1.41.

Front

How do you determine the range for estimating √8?

Back

To estimate √8, find the perfect squares it lies between: 2^2 (4) and 3^2 (9). Thus, √8 is between 2.8 and 2.9.