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The lengths of the legs of a right triangle are 8 centimeters and 12 centimeters. Express the length of the hypotenuse in simplest radical form.

4$\sqrt{13}$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 3

Simplifying Radicals

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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The length of the hypotenu…

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The length of one leg of a…

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One leg of a right triangl…

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USING THE PYTHAGOREAN THEO…

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Algebra An 8-inch-long alt…

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given here the lengths of the legs of a right triangle are 87 years in 12 centimeters. Okay, so here's a right triangle. Here's our two legs. Seven the length of the iPod news. Well, we know that by Pythagorean theorem, right that we know that eight squared plus 12 square is going to be equal to of this length. We call it Let's call it art cortex. So it's equal to while X squared. So I'm a square. That's gonna be 64 right? So you have 64 plus 12 square is going to be 100 and 44 so we have 64 plus 144 is equal to X squared. So therefore so what is 64 plus 144 is gonna be equal. Teoh 208. So we have 208 is equal to X squared. So what is Exe Um that's where it acts. 208 is equal. Oops. It is equal to X squared. OK, so 208 is equal to X squared. That means that X is gonna be equal to the square root of 208. Okay, so now I want to go ahead and try and simplify. This is the square root of 208. Is there a perfect square? Such that that number times itself is gonna be equal to 200 eat? Um, let's see. 200 aids is 16. Yes, 16 times 13 is actually 208. So we have exited equal to the square root off while 16 times 13. But the square 16 is four. That can come outside of your square root. So therefore, this is equal to four times the square root of 13. There's no answer. And of course, this is in well, centimeters, right? So he here is our answer. All right, take care.

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