MATH SOLVE

2 months ago

Q:
# Which is the irrational number?[tex]-\frac{16}{4}[/tex], [tex]\sqrt[3]{64}[/tex], [tex]\frac{15}{8}[/tex], or [tex]\sqrt{26}[/tex]

Accepted Solution

A:

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, β(64), well 4Β³ = 64, thus β(64) = β(4Β³) = 4, and we can write any integer is over 1, namely 4/1, so that's rational.[tex]\bf \sqrt{26}\implies \sqrt{2\cdot 13}\implies \sqrt{2}\cdot \sqrt{13}[/tex]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, β2 times another irrational value β13 in this case, so, no way we can express those in a rational fashion.factoid:Ancient Greeks were aware of β2 as irrational, and kinda never liked it very much, thus they didn't deal with it much.