in-3-10-tell-whether-each-represents-a-number-that-is-rational-irrational-or-neither-sqrt025

Question

In $3-10,$ tell whether each represents a number that is rational, irrational, or neither.
$$
\sqrt{0.25}
$$

Dilip Paruchuri · Accepted Answer

all right. Hey, guys. So this problem, we have the square root of 0.25 Where, after the rational, irrational or neither first step, let&#x27;s simplify this or at least try to simplify it. So we have square root of 0.250 point 25 Looks like a perfect square. Let&#x27;s find out if it is a perfect square. So 0.25 I can be written as a product of 0.5 times 0.5 and from this we see that it actually is 0.25 is a perfect square. In a sense, so we have can simplify this a square of 0.5 square. When you square roots something square, you just get that something. So you&#x27;re left with 0.5. And so we&#x27;re saying that square root 0.25 is equal to 0.5 point five is a rational number because it can be written as a fraction. Its fraction equivalent is 1/2. So we know that 0.5 is ah, rational number. That means you&#x27;re a 0.2 square 0.25 which is equal to 0.5 is a rational number as well. And from this easy to say that this value right here is equal into a rational value. And just to recap, the key step that we made is that we factored out. We basically rewrote our 0.25 as a product of Europe with five times your 50.5. Then we realized it was a perfect square. Made our life a lot easier to determine that it was rational. Thanks.

James Kiss · Answer

because the square root of 25 is equal to the square root of five. Squared five squared is 25 and it&#x27;s heard of five. Squared is equal to five because the square root and squares are in verses of each other and by could be written as 5/1. So by the definition of a rational number, since it can be written as a fraction, that means the skirt 25 is rational.

James Kiss · Answer

there has to determine if the scared of zero is rational or irrational or neither, and since the skirt of zero is equal to zero and zero could be written as a fraction with any of them, I&#x27;m a besides zero. Since it&#x27;s written as a fraction, it is rational.

Dilip Paruchuri · Answer

all right. Hey, guys. So this problem, we have the fourth route off 16. So basically, what we&#x27;re trying to do is determine if this value if this thing simplifies to irrational, irrational or neither value and first step, is that we&#x27;re going to try to simplify our four through eight of 16. We know 16 is the product of four times for, so let&#x27;s write that as that. So so cube so forth. Fruit of 16 is equal to four through of four times four. We also know that four can be written as two times two, so let&#x27;s rewrite each four as the product of two times, too. You have two times two times two times two. So you&#x27;re multiplying two together by itself for times. And another way to write that is as an exponents. So it&#x27;s Equus. Over two times, two times two times two is equal to two to the fourth, 40 minutes 16 is equal to four. Threw it off to to the fourth. And when you have the fourth root of something to the fourth, it&#x27;s just equal to that something. So this is just equal to two, and so we have four through of 16 is equal to two. We know two is a rational number so forth. Fruit of 16 is also a rational value.

Dilip Paruchuri · Answer

all right. Hey, guys. So in this problem, we are giving the square root of feet and we&#x27;re being asked if the square root of eight is a rational, irrational or neither we that we can determine. So let&#x27;s take a look at the squirt of eight. Now, the square root of eight weekend basically rewrite as the square root of four times two square root of four times to just algebraic steps is a square to four times the square root of two we know for is a perfect squared. Two squared is equal to four, and basically what that means is square root of four can be simplified to just two. So in a sense, squared of eight is equal to two times square root of two. And now, if we take a look at this simplification, squirt of eight is equal to two times word of two. And in that case we know that two is a rational, rational number, and we also know that square root, too, is an irrational number. So Squared eight is what I would like to say is a rational multiplied by an irrational, and this is a fact that&#x27;s gonna be very important in this chat in this section and that section, and that fact is that whenever you&#x27;re multiplying a rational, by and irrational, you&#x27;re always going to get an irrational value. So in that case, we can death definitively say that since Square eight is the product of an irrational of and ration of eight. Sorry, since Square eight is the product of a rational and an irrational, we can definitively say that&#x27;s where the eight is an irrational value. So thanks for listening, guys. And I hope this helped. And please do remember the key factor that irrational times an irrational always gives us an irrational.

James Kiss · Answer

were asked to determine if the spirit of negative eight is rational or irrational. Well, since the squared of negative eight is imaginary graze the imaginary Route of eight, which could be broken down to two times imaginary root of two. That&#x27;s a little bit irrelevant in this question because we&#x27;re asked, determine if a spirit of negative eight is rational or irrational, Rational and irrational numbers fall under the rial number system and this is imaginary, so it is neither a little bit tricky.

Problem

In $11-38,$ evaluate each expression in the set o…

Problem 10 Easy Difficulty

In $3-10,$ tell whether each represents a number that is rational, irrational, or neither.
$$
\sqrt{0.25}
$$

Answer

rational

Related Courses

Algebra 2 and Trigonometry

Related Topics

Discussion

Top Educators

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Ann Xavier Gantert

Algebra 2 and Trigonometry

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

rational

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry