Question

Which is the irrational number?

$-\frac{16}{4}$, $\sqrt[3]{64}$, $\frac{15}{8}$, or $\sqrt{26}$

Answer 1

a rational value is a value that can be expressed as a ration or fraction, so -16/4 and 15/8 are pretty much there already so we can skip those two.

now let's take a peek at the roots, ∛(64), well 4³ = 64, thus ∛(64) = ∛(4³) = 4, and we can write any integer is over 1, namely 4/1, so that's rational.

$\bf \sqrt{26}\implies \sqrt{2\cdot 13}\implies \sqrt{2}\cdot \sqrt{13}$

well, 2 and 13 are both prime numbers, so they can't be factored into two values that will ever give either one, so we have one irrational value, √2 times another irrational value √13 in this case, so, no way we can express those in a rational fashion.

factoid:

Ancient Greeks were aware of √2 as irrational, and kinda never liked it very much, thus they didn't deal with it much.