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In $3-14,$ determine whether each of the numbers is rational or irrational.$$\sqrt{17}$$

irrational

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Chapter 3

REAL NUMBERS AND RADICALS

Section 1

The Real Numbers and Absolute Value

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $3-14,$ determine wheth…

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all right. Hey, guys. So in this problem, we're given the square root of 17 and we're being asked to determine if this is a rational or irrational number. Show again. Square roots. What happens with square roots is most of the time. It's easy to tell if a square root is irrational or rational, because the square root can only be rational. If you're taking the square root of a perfect square on the perfect square is anything of the form Here, let me write this in different color. So perfect square is anything of the form of a square, some number a squared. And when you take the square root of a squared a squared, you're left with a and we're way. We assume that this is rational, Uh, and, uh, and basically, when we say that a is rash on this game case and we're assuming that in this first step right here, we're squaring a rational number. That's just a little basic assumption that we're making. But in general, when you have the square root of a number, it's it's rational. If you're taking the square root of a perfect square and right here, we're taking the square root of 17. And if we just list are perfect squares right here, we get zero squared to 01 square is 12 squared is too. Three squared is nine. Four, squared is 16 and five, squared is 25 and now square root of 17 fits in between four and five, so we know that it's a four point something. And Norman, when you take the square root of a non perfect square, it is. And it is an infinite decimal that is non repeating. There is no pattern, so this is the decimal. So I think I swear to something is something like 4.1 to blah, blah, blah, blah. It's a school. It's an infinite and non repeating decimal. And as we can see right here from this, we can see that swear word of 17 is an irrational number. Thanks for listening, guys, and I hope this helps

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