Which of these numbers are irrational? -4,-4/5,0,0.1,square root of 5, 2.3, and square root of 25

Question

There can be more than one answer.  Thanks in advance.

Answer 1

And irrational number is one that cannot be expressed as the ratio of two integers. 

Every one in the list can be so expressed except for √5.

 

Answer 2

Hi Anna,

 

An irrational number is a number that can't be written as a ratio of integers (whole numbers). Any integer can be written as a ratio of numbers: take -4 = -4/1, for example, or 6 = 12/2. So integers are never irrational.

 

Since any terminating decimal can be written as a ratio of numbers -- 0.44 = 44/100, for example -- a decimal has to be nonterminating for it to be irrational. Nonterminating means it goes on forever, like pi, and unlike 2.3.

 

What does that mean for the numbers you have? For numbers like the square root of 5, you will have to plug that into a calculator to see if it is terminating or not.