Video: Identifying the Position of Irrational Numbers on a Number Line

Identify which arrow represents the position of √24 on the number line.

01:31

Video Transcript

Identify which arrow represents the position of the square root of 24 on the number line.

We recall that squaring and square rooting are inverse operations. Four squared is equal to 16 as four multiplied by four is 16. This means that the square root of 16 is equal to four. This means that the radical, the square root of 16, will be at the same place on the number line as four. Repeating this process for our other integer value five, we have five squared is equal to 25, which means that the square root of 25 is five.

In this question, we need to identify whether arrow a or arrow b represents the square root of 24. As 24 lies between 16 and 25, the square root of 24 must be greater than the square root of 16 and less than the square root of 25. This means the square root of 24 lies between the integers four and five. 24 is closer to 25 than 16. Therefore, the square root of 24 will lie closer to five than it does to four. The correct answer is, therefore, arrow b.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.