# Video: Ordering Rational and Irrational Numbers

Without using a calculator, order the numbers 4, 5, and √19 from smallest to largest.

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### Video Transcript

Without using a calculator, order the numbers four, five, and root 19 from smallest to largest.

Okay so to solve this problem, we’ve got three numbers: four, five, and root 19. The number we need to look at is root 19 cause we need to work out the value of this number. So in order to help us solve this problem, what I’ve done is I’ve listed the first few square numbers. So we’ve got one, four, nine, 16, 25, and 36. And we get these square numbers by multiplying a number by itself. So one multiplied by one is one. Two multiplied by two is four. Three multiplied by three is nine, etc.

So if we look at number 19, we see that the number 19 actually fits between 16 and 25. So therefore we can say that root 19 is going to be greater than root 16 but less than root 25. Well root 16 is equal to four because four multiplied by four gives us 16. And root 25 is equal to five because five multiplied by five gives us 25.

So therefore, we can say that root 19 is greater than four but less than five. So now we can order our numbers, remembering that the question asks us to do it from smallest to largest. And we’re going to get four, root 19, and five. And we get that and know that because we found that root 19 was between four and five.