Understanding the Truth behind 2 ≥ √2

Thread starter brycenrg
Start date Sep 12, 2015
Tags

Root Square Square root

In summary, "2 >= square root 2" is a mathematical inequality that compares the values of 2 and the square root of 2. It is a true statement because 2 is greater than or equal to 1.414, the value of the square root of 2. This can be proven using basic algebra by squaring both sides of the inequality. In mathematics, this inequality is a fundamental principle and has applications in fields such as geometry and calculus. One real-life example of "2 >= square root 2" is the relationship between the diagonal and side length of a square.

Sep 12, 2015

brycenrg

Why is this true? It is bigger but it is not equal to

Mathematics news on Phys.org

Sep 12, 2015

axmls

The symbol is read "Greater than or equal to."

Sep 13, 2015

brycenrg

Thank you :)

Sep 13, 2015

pbuk

Science Advisor

Homework Helper

Gold Member

Note that except when writing computer code or in a plain text environment you should always use the ≥ symbol (LaTeX \ge ## \ge ##), or when writing by hand alternatively ## \geqslant ##.

Related to Understanding the Truth behind 2 ≥ √2

1. What does "2 >= square root 2" mean?

The expression "2 >= square root 2" is a mathematical inequality that compares the values of 2 and the square root of 2. The symbol ">=" means "greater than or equal to", so this expression can be read as "2 is greater than or equal to the square root of 2".

2. Is "2 >= square root 2" a true statement?

Yes, "2 >= square root 2" is a true statement. This is because the value of the square root of 2 is approximately 1.414, and 2 is equal to itself. Since 2 is greater than or equal to 1.414, the statement is true.

3. How can you prove that "2 >= square root 2" is true?

This inequality can be proven using basic algebra. We can square both sides of the inequality, which does not change the truth of the statement. This results in 4 >= 2, which is a true statement. Therefore, if 4 is greater than or equal to 2, then 2 must also be greater than or equal to the square root of 2.

4. What is the significance of "2 >= square root 2" in mathematics?

The inequality "2 >= square root 2" is one of the fundamental principles of mathematics. It is an example of the concept of a real number being greater than or equal to its square root. This concept is used in many mathematical proofs and has important applications in fields such as geometry and calculus.

5. Can you provide a real-life example of "2 >= square root 2"?

One example of "2 >= square root 2" in real life is the relationship between the diagonal and side length of a square. The diagonal of a square with side length 2 is equal to the square root of 2 times the side length. This means that the diagonal, which is approximately 2.828, is greater than or equal to the side length of 2. This can be expressed as "2 >= square root 2" and illustrates the concept of a real number being greater than or equal to its square root.