Is the square root of two over 8 rational or *irrational

2/8 = 1/4

since √4 = 2, what do you think?

on the other hand, (√2)/8 is irrational

I dont really get what your saying I would think that it would be irrational since the square root of 2 is irrational

1/4 = 1/2 * 1/2 = (1/2)^2

so,
√(2/8) = √(1/4) = √(1/2)^2 = 1/2
rational

so how do you know that it is irrational plz help

To determine whether the square root of two over eight is rational or irrational, we need to simplify the expression first.

The square root of a number is the value that, when multiplied by itself, gives the original number. In this case, the square root of two is written as √2.

To simplify √2 / 8, we can rewrite the expression as √2 * 1/8, which is equal to (1/8)√2.

Now, let's consider the definition of rational and irrational numbers:

- A rational number is any number that can be expressed as the quotient (or fraction) of two integers. For example, ½ and 3/4 are rational numbers.

- An irrational number is a number that cannot be expressed as a fraction of two integers. Instead, it has an infinite non-repeating decimal representation. Examples of irrational numbers include π (pi) and √2.

In our case, (1/8)√2 is a rational number because it can be expressed as the product of a rational number (1/8) and the irrational number (√2). Thus, the square root of two over eight is rational.