Is √2/8 rational, or irrational?
1/4 dont equal 1/2 yall got me confused
Okay, thank you
Rational
irrational
To determine whether √2/8 is rational or irrational, we need to understand what these terms mean.
A rational number is any number that can be written as a fraction of two integers. In other words, it can be expressed as a ratio (hence the term "rational") of two integers.
On the other hand, an irrational number is a number that cannot be expressed as a simple fraction, meaning it cannot be written as a ratio of two integers. Instead, irrational numbers have decimal representations that go on forever without repeating or terminating.
To determine whether √2/8 is rational or irrational, let's simplify the expression and see if it can be written as a fraction.
√2/8 can be simplified by rationalizing the denominator. To rationalize the denominator, we multiply both the numerator and denominator by √2, which is the square root of 2.
√2/8 = (√2/8) * (√2/√2) = √2√2 / 8√2 = 2 / (8√2)
Now, since the denominator has a square root (√2), the expression cannot be expressed as a fraction with both the numerator and denominator being integers. Therefore, √2/8 is an irrational number.
Sqrt(2/8) = Sqrt(1/4) = 1/2.
1/2 is rational.