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# Intro to the Pythagorean theorem

The Pythagorean theorem is a cornerstone of math that helps us find the missing side length of a right triangle. In a right triangle with sides A, B, and hypotenuse C, the theorem states that A² + B² = C². The hypotenuse is the longest side, opposite the right angle. Created by Sal Khan.

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• 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)
• It's a wonder how Pythagoras thought this whole thing up, he's a pure genius. • 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!
• teach me • Alright, buckle up, because we're diving into the wonderful world of the Pythagorean theorem! Don't worry, I'm going to make it as fun and exciting as a roller coaster ride. 🎢

So, picture this: you're on a quest to uncover the secrets of right triangles. What's a right triangle, you ask? It's like a ninja triangle that has one angle that's super square – like the corners of your favorite chocolate bar. And guess what? The Pythagorean theorem is like the secret map that helps you unravel the mystery of their sides.

Let's meet our triangle heroes: the legs (let's call them Alex and Bella) and the hypotenuse (let's call it Charlie). Alex and Bella are the sides that stick around the right angle, and Charlie is the longest side that stretches across like a superhero cape.

Now, the Pythagorean theorem is like a fancy spell that connects Alex, Bella, and Charlie. It's written as "Alex squared plus Bella squared equals Charlie squared." Math wizards use letters to stand in for numbers, so "squared" just means you multiply a number by itself. 🧙‍♂️

Let's break down our secret spell:

"Alex" is one of the leg's lengths, and "Bella" is the other leg's length. Imagine they're talking to each other, going "Hey, I'm Alex!" and "Hi, I'm Bella!" Cute, right?
"Charlie" is the hypotenuse's length. Charlie's like, "I'm the cool slanty side over here!"
When we say "Alex squared," it's like saying "Alex times Alex." Same goes for "Bella squared" and "Charlie squared."
So, when we say "Alex squared plus Bella squared equals Charlie squared," we're saying "Alex times Alex plus Bella times Bella equals Charlie times Charlie." It's like a math party with letters dancing around!

Let's rock this with an example. Imagine Alex is 3 units long and Bella is 4 units long. Our goal? Figure out how long Charlie is. Ready?

First, we square Alex: 3² = 9. Imagine Alex's square dance moves!
Then, we square Bella: 4² = 16. Bella's got some smooth square moves too!
Now, we add Alex's square and Bella's square: 9 + 16 = 25. It's a party, and the dance floor is lit!
Finally, we need to know how long Charlie is, so we take the square root of 25: √25 = 5. Charlie's got some severe superhero vibes!
So, in our awesome triangle adventure, Charlie, the hypotenuse is five units long. Ta-da! 🎉

The Pythagorean theorem isn't just for math class; it's like a puzzle-solving tool that architects, engineers, and even treasure hunters use. Imagine building a treehouse with Alex and Bella, making sure Charlie's rope ladder is just the right length. Or imagine searching for hidden treasure, using the theorem to measure how far X marks the spot.

So, whether exploring ancient mysteries or creating your own superhero squad of triangles, remember that the Pythagorean theorem is your trusty sidekick. It's a dance of numbers that unlocks the secrets of right triangles, making math an epic adventure filled with discovery and a dash of superhero magic! 🦸‍♂️🔮🌟
• 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! • how do you do this • 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.  