What kind of number is square root of 2

If D is equal to one 1 , then it is an integer. Therefore, every integer is a rational number. The set of all rational numbers is usually represented as Q. A decimal number is a rational number if it terminates has a finite number of digits or repeats a finite sequence of digits.

These statements hold true for any integer base number binary, hexadecimal, Numbers that do not terminate as a decimal number. Real numbers include rational numbers integers, fractions and irrational numbers. Since any fraction has an equivalent fraction in lowest terms, we can assume is in lowest terms i. Someone must have already come by and simplified it for us. We'll have to send them a card. Okay, check this out: b is an integer, right? It would have to be, since we assumed at the beginning that is a rational number, which means a and b were both integers.

So b 2 is also an integer, 'cause we're not gonna get a fraction or decimal when we square an integer. So since , we know a 2 is 2 times some integer b 2. That means a 2 is an even number; 2 times any integer is an even number. This means a must also be even think about it—whenever you square an even number, the result is always even.

Now that that's settled, let's show that b has to be even. We do have a point, and we are getting to it. Bear with us. This means b must be even, for the same reasons that a had to be even. Come on, b , that's not cool—come up with your own reasons. But if both a and b are even, then 2 would divide both a and b , which means the fraction isn't in lowest terms.

And they thought the number line was made up entirely of fractions, because for any two fractions we can always find a fraction in between them so we can look closer and closer at the number line and find more and more fractions.

So because this process has no end, there are infinitely many such points. And that seems to fill up the number line, doesn't it? And they were very happy with that The square root of 2 is "irrational" cannot be written as a fraction Hide Ads About Ads. Let us assume that it is, and see what happens. Which is close to 2, but not quite right You can see we really want m 2 to be twice n 2 is about twice