By definition, a rational number is a precise number: or in other terms, we know its exact value. Irrational numbers are number that has endless digits on the right of the decimal points: in other terms, we can't know its exact value.
First question:
√2.5 = 1.58113.... It's endless, so irrational.
-√64 = -8 it's a whole number, so rational.
4√5 = 8.94427.... Endless, so irrational.
√14.4 = 3.7947... Endless so irrational.
So -√64 is the rational number.
Second:
7.885 is rational because has a defined number of digits after the decimal points.
π² = 9.8696.... Endless, so irrational.
√0.144 = 0.3794.... Endless, so irrational
√91 = 9.5393.... Endless, so irrational
So 7.885 is the rational number.
Third:
-7.8 bar: You can notice the line over the 8, this means that there's an infinite number of 8 after the decimal points. So it's 7.88888888888.... Endless, so irrational.
√25 = 5, whole number so rational
25.8125 Has a definite number of digits after the decimal point, so is rational.
√0.025 = 0.1581... Endless, so irrational.
So -7.8 bar and √0.025 are irrational.
Fourth:
π= 3.1415... Endless, so irrational.
1.425 has a definite number of digits after the decimal point, so rational.
√50 = 7.0710.... Endless, so irrational
√-4 Doesn't exist. Finding the square root of a negative number is mathematically impossible.
So 1.425 is the rational number.
Fifth:
√10 = 3.1622..... Endless, so irrational.
√100 = 10, a whole number so rational.
√1000 = 31.6227..... Endless, so irrational
√100000 = 316.2277...... Endless, so irrational.
√100 is the rational number.
Hope this helps!! :D And I hope you understood the lesson a bit more xD