Pythagorean TheoremPythagoras (puh thag or us) was a Greek philosopher and mathematician, born in Samos in the sixth century, B.C. He and his followers tried to explain everything with numbers. We remember him today mainly for his equation relating the lengths of the legs of a right triangle to the length of its hypotenuse.
The Pythagorean (puh thag or ee un) Theorem, also called the Pythagorean Property, says that the sum of the squares of the lengths of the legs of any right triangle is equal to the square of the length of the hypotenuse, Another way of looking at the Pythagorean Theorem is to think about actual squares of the lengths of the sides of a right triangle. 



Pythagorean Triples are groups of three whole numbers that make the Pythagorean Theorem true (and therefore define a true right triangle). 3, 4, and 5 are a Pythagorean Triple. There are several ways to generate Pythagorean Triples. Here are two:




You can appropriately ask students to use the Pythagorean Theorem
When you work with the Pythagorean Theorem, numbers may get quite messy. Have your students compute without units, then attach the units after they find the numerical part of the answer. There are two ways to show answers to a problem involving square roots. For example, find the length of the hypotenuse for this right triangle. 



You have values for a and b in the equation Both the simplified radical form and the approximation for the answer to the computation should be acceptable answers. In radical form, the answer is exact. However, if the value under the radical is not a perfect square, its square root is approximate and must carry the wavy equals symbol. Most calculators will give approximations for square roots. If you do not have calculators available, use a table of square roots. The answer to the original problem is: The hypotenuse is 25 centimeters long or The hypotenuse is about 4.5 centimeters long. How to Simplify Inside a Radical If a number in radical form is not a perfect square, you may be able to simplify that number by factoring. Here are some ways you can show answers to problems involving square roots.
Since 125 is not a perfect square, its square root is not a rational number. However,
Since 41 is not a perfect square and does not have any factors that are perfect squares, 41 cannot be simplified. 
