Hello! My question is 'Is the Square Root of two over 8 a rational or irrational number? At first I thought it was rational because it was written as a fraction, which I thought meant it was rational, but then I realized the square root of two is irrational so wouldn't that make the whole thing irrational. I have reread the lesson, the textbook, and watched a few videos on the subject, and am leaning towards it being irrational, but I'm still confused. If anyone knows a website that can help me, or if the fact that the square root is irrational affects if the whole thing is irrational, I would greatly appreciate it!

Thank you so much! This really helped!

it is irrational. And since 8 is a non-square, the square root of 8 is irrational

Hello! Good observation on recognizing that the square root of two is an irrational number. To answer your question, let's break it down step-by-step.

First, we need to determine if the square root of two over 8 is rational or irrational.

The square root of two (√2) is an irrational number. This means it cannot be written as a fraction or a quotient of two integers. Therefore, if the expression only contained √2, then the answer would be irrational.

But in this case, we also have it divided by 8. To determine if the whole expression is rational or irrational, we can use the fact that the division of a rational number by a non-zero rational number results in a rational number.

Since 8 is a rational number (it can be written as the fraction 8/1), we can conclude that √2/8 is rational.

In summary, √2/8 is a rational number.

As for the website recommendation, one useful resource to check out is Khan Academy (www.khanacademy.org). They provide comprehensive explanations and examples on various mathematical topics, including rational and irrational numbers.