in-3-14-determine-whether-each-of-the-numbers-is-rational-or-irrational-sqrt35

Question

In $3-14,$ determine whether each of the numbers is rational or irrational.
$$
\sqrt{3}+5
$$

Leina Wu · Accepted Answer

God, this is question number nine. We&#x27;re trying to determine if the root of three plus five is rational or irrational. Not five is rational. Room three. We know this is irrational. It&#x27;s true. So when we act, it&#x27;s a rash number with rational number. We got an irrational number because this a group of three plus five could not be returned as any fracture. This is irrational.

Dilip Paruchuri · Answer

our guys in this problem. We have the values square root by divided by square route five and we&#x27;re being asked to determine if this value is an irrational number or a rational number. And the first step we&#x27;re going to do is we&#x27;re going to simplify the square. We&#x27;re gonna simplify square root 50 divided by square root five. And what we&#x27;re going to do first is we&#x27;re going to rewrite it. So let&#x27;s take a step back. Different color pen. So we have the square root of five, divided by the square root of five that is the same thing as a square root off. Five over five Justin Algebraic Step right here and the next up there were Hindus would do five, divided by 55 Divided by five is one, and we&#x27;re taking the square root of one. And when you take the square root of 11 is a perfect square one. Basically, this is the same thing as square root of one squared the square root, and the square cancels out. So you&#x27;re left with is just one and one by definition is a rational number. And since square with a five over five. Square 25 is equal to one. We know that this value right here this this whatever this value square defy over square 25 is a rational number. So let me recap that right. Really quickly. So the value that we found for when we simplified square root of five over square 25 is one which is a rational number. And since one is a rational number and one is equal to square 25 divided by scores of five, we can say that square with a five over Swear to five is a rational number. Okay, guys, I hope this help clarify some doubts because basically what we had to do was we just simplified whatever expression they gave us and determine if it was rational or irrational. And I hope this helps all the

Dilip Paruchuri · Answer

all right. Hey, guys. So in this problem, we are given two and 1/3 plus square root three and were asked, determine if this is rational or irrational. And so first, what we&#x27;re going to do is we see that this involves the sum of two numbers. And since we already know some things about something rational and irrational numbers, we&#x27;re gonna classify each of these individual components of some as rational or irrational and then decide whether the sum is irrational, rational. So first step let&#x27;s take a look at each of the components in the sum to 1/3 to 1/3 is equal to 2.3 repeat, and 2.3 repeat is a repeating. It is a repeating decimal, and it could also be written as a fraction. So we know that this number is a rational number. However, when we take a look at square root three square with three equals 1.73 blah blah, blah blah. It&#x27;s an infinite number that&#x27;s non repeating, and we know that this is an irrational number. So basically, in this, some were summing a rational, so we&#x27;re basically something irrational, plus and irrational and from our previous problems. We know for a fact that whenever you some of rational and an irrational number, you are going to get an irrational value. That&#x27;s just a fact and big due to this fact. We can determine that two on 1/3 plus square root three is indeed gives us an irrational value. Thanks for listening, guys. And I hope this helps office problem.

Dilip Paruchuri · Answer

all right. Hey, guys. So in this problem, we&#x27;re given the square root of 17 and we&#x27;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&#x27;s easy to tell if a square root is irrational or rational, because the square root can only be rational. If you&#x27;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&#x27;re left with a and we&#x27;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&#x27;re assuming that in this first step right here, we&#x27;re squaring a rational number. That&#x27;s just a little basic assumption that we&#x27;re making. But in general, when you have the square root of a number, it&#x27;s it&#x27;s rational. If you&#x27;re taking the square root of a perfect square and right here, we&#x27;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&#x27;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&#x27;s a school. It&#x27;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

Dilip Paruchuri · Answer

all right. Hey, guys. So in this problem, we have the square root of two divided by two, and we&#x27;re being asked to determine if, uh this value squared of two over two is irrational or rational. And in order to determine this, let&#x27;s break this down. Distraction, dishonest into its numerator and denominator. So it&#x27;s numerator is square root too and square root to you&#x27;re taking the square root of a number. And in the previous, uh, problem that I just went over, I said that if you take a square root of a number that the square root of a number is only gonna be irrational. If you&#x27;re taking the square root of a perfect square and square root to the two, we know that it is not a perfect square and square to is. Indeed if you cut later out out, it&#x27;s something like 1.7412 blah, blah, blah. It&#x27;s an infinite, non repeating decimal, and that makes it an irrational value, an irrational value. And now, if you take a look at the denominator, denominator is the value two and two it is, and it is a finite decimal because it&#x27;s like 2.0, it&#x27;s still a finite decimal, and it is non repeating. It&#x27;s Ah, it&#x27;s a finite decimal. We don&#x27;t have to worry about the repeating part because it can be put over as a fraction it is to over one, and that&#x27;s what makes it a rational number. And basically, in this problem we&#x27;re dividing an irrational by rational number. And what I&#x27;m telling you now is a fact that is always going to be true. When you divide an irrational number by rational number, you are always going to get a an irrational number. So in irrational, divided by a rash is going to give you an irrational number and in this case, are irrational is route to and our rationalist too. So that value that we&#x27;re going to get is an irrational value. And so because of this, we can decisively say that square root to over two is an irrational value. Thanks for listening, guys, and I hope this helps solve this problem

Kendra Jones · Answer

in this example were asked to determine if the square root of 16/2 is rational or irrational. Rational and irrational names are what we use to determine can classify different numbers. Let&#x27;s talk about the definition of each. Before we classify this number, A rational number is a whole number. It is a decimal, or it is a fraction. An irrational number cannot be written as a whole number if it is a decimal than it will not repeat or end an example of an irrational number that is a decimal is pie, which never repeats for ends. And then we cannot write an irrational number as a fraction with an integer on top and bottom. So let&#x27;s now classify the square root of 16/2. Let&#x27;s simplify if possible. The squared of 16 gives us a whole number of four, because four times for 16 and two was our denominator. Now, already we can see this is rational because for over two is a fraction, which is considered rational. Let&#x27;s simplify this all the way. 4/2 or four, divided by two, is the same as 22 and two. As a simplified as we can get, two is a whole number, so again rational. So we would classify this as a rational number

Problem

In $3-14,$ determine whether each of the numbers …

Problem 9 Easy Difficulty

In $3-14,$ determine whether each of the numbers is rational or irrational.
$$
\sqrt{3}+5
$$

Answer

irrational

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