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
