Question

I NEED HELP PLEASE !!!!

Answer 1

Answer:

See below

Step-by-step explanation:

So we have the following six values:

$77.65488139\\\sqrt{0.156}\\368. 5468432...\\253,897,615.\bar3\\14.19274128...\\\\\sqrt{\frac{4}{9} }$

And we want to determine which are irrational.

Recall what irrational numbers, are they are numbers that do not repeat nor terminate. In other words, they never end, and their digits never repeat.

So, let's go through each one.

77.65488139 is rational. Yes, it has a lot of decimal places but notice there are no ellipses after it. Thus, it terminates and is rational.

√(0.156) is about (use a calculator) 0.39496835... It is not repeating nor does it end. Thus, √(0.156) is irrational.

368.5468432... has the ellipses. Thus, it doesn't repeat and doesn't terminate. It's irrational.

253,897,615.3 has a bar over the 3 at the end. This means that this repeats. Therefore, while it doesn't terminate, it is rational.

14.19274128... has an ellipses. It doesn't repeat nor terminate. It's irrational.

Lastly, the square root can be simplified to 2/3. This is approximately .6666... While this doesn't terminate, it repeats, so it's rational.

Edit: Grammar