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

Kathryn Kingham

Identify which of the arrows represents the position of √30.

01:16

Video Transcript

Identify which of the following arrows represents the position of the square root of 30.

To estimate the square root of 30, I’m going to think of squares that I already know. I know that three squared equals nine. I know that five squared equals 25. And I know that seven squared equals 49. And I know the square roots that correspond to these. The square root of nine is three, the square root of 25 is five, the square root of 49 is seven. The square root of 25 is five, and the square root of 49 is seven.

The square root of 30 must fall somewhere between the square root of 25 and the square root of 49. And we only have one arrow that falls between five and seven on this line; it’s b.

The b arrow on the graph is a good representation for the square root of 30.