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# Intro to the Pythagorean theorem

Sal introduces the famous and super important Pythagorean theorem! Created by Sal Khan.

## Want to join the conversation?

• close towards the end how did you solve the square root?
• you do the principal root:the square root of 2*54=the square root of 108 and the square root of 2*27=the square root of 54 and the square root of 3*9=the square root of 27 and the square root of 3*3=the square root of 9 and 2*2*3*3*3=108/the square root of 2*2*3*3*3=the square root of 108.
• how you know which one is A,B, or C?
• c is equal to the hypotenuse and a and b are the shorter sides (you can choose which one you want to be a or b)
• What is the Pythagorean theorem?I need help trying to understand it.
• The Pythagorean theorem consists of a formula a^2+b^2=c^2 which is used to figure out the value of (mostly) the hypotenuse in a right triangle. The a and b are the 2 "non-hypotenuse" sides of the triangle (Opposite and Adjacent). Once you progress, you will be given the hypotenuse and would be needed to find the opposite or the adjacent side (a or b). The Pythagorean theorem is a simple formula which uses the squared value of a and b; for example "a=3 and b=4, what is the value of c?" you square a (3^2=9=a) and b (4^2=16=b) and add the 2 values (9+16=25) to get to c. To complete the question, you have to square root c's value (square root of 25=5) because the formula says c^2 and not just c. Once you have done that, you can check your answer by squaring a,b and c to see if you have added and divided (Square-rooted) correctly.

Hope this helps!
• It's a wonder how Pythagoras thought this whole thing up, he's a pure genius.
• It is now shown that this was known long before Pythagoras, he just got the credit for other people's work. Further, he did not really like the idea of irrational numbers which is a consequence of the theorem. Interesting article on this is at https://www.britannica.com/science/Pythagorean-theorem which also talks about his life and how he may have come into contact with those who already had applied the Theorem.
• Hi, I have a question. What is the square root? In the video at he said that in order to complete the equation you have to take the positive square root of both sides, which for 25 would equal 5. But what does that mean? How did he get 5 from 25? What did he do, what did he divide 25 by and why did he divide that and not another number? I will be waiting for a response thank you to those that reply, I will be very thankful because I know I would be taking time away from you just so you can answer my question. Thanks!
• A square root is a number that produces a specified quantity when multiplied by itself.
It goes hand in hand with exponents and squares. 2 squared is 4, and the square root of 4 is 2.
The square root is just the number that, when multiplied by itself, equals the original number you are starting with.
The square root of 25 is 5. Because 5 * 5 is equal to 25.
The square root of 49 is 7. Because 7 * 7 is 49.
The square root of 625 is 25. Because 25 * 25 is equal to 625.
The square root of 89,737,543 is 9473. (Approximately)
If you still have trouble with this concept:
• 8=1 that is how it needs to be
• Couldn't you have just solved 6 squared + b squared = 12 squared using an equation? Or doing 12 squared minus 6 squared??
• Tell me if I'm wrong, but I think this is exactly what Sal does in the video. He explains the theorem and the formula, then applies it by taking a problem and turning it into an equation.
• This doesn't have much to do with the video, but at , Sal says we take the positive square root of both sides. Is there a negative square root?
• Yes, for example, the positive square root of 25 is 5 and the negative square root is -5. When you square negative numbers, you get a positive answer, therefore the square root of a positive number will have both a positive and a negative.
• I still don't really get how to do this problem. Can somebody maybe help?
• A^2 + B^2 = C^2 Is the Pythagorean Theorem
A and B are one of the "legs" of the triangle, and C is the hypotenuse. How about you try plugging in some values yourself?
• At , why does it have to be a right triangle?
• Good Question!
For the Pythagorean Theorem to work it needs to be a right triangle because......
The formula: a^2+b^2=c^2
tells us to square the smaller sides and the hypotenuse(largest side)
if you put the to smaller squares on top of the larger square they would be the same
This would not be the same if it was not a right triangle

Ex:
Triangles side lengths: 10 (hypotenuse), 8, 6
a^2+b^2=c^2
(8)^2+(6)^2=(10)^2
64+36=100
NOTE: The numbers represent the area of the square (64 square units , 36 square units, and 100 square units)
100=100

I hope this answer helped!
Pls. comment if confused
If I still cannot help i am sure another person can clear this up
Pls. comment if i made a mistake
Thanks!