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

Identify which of the arrows represents the position of √(51).

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Video Transcript

Identify which of the arrows represents the position of the square root of 51.

Square-rooting is the opposite of squaring a number. So it is worth writing out our square numbers first. Three squared is equal to nine, as three multiplied by three is nine. Four squared is equal to 16, as four multiplied by four is 16. The square of the integers from five to 10 are 25, 36, 49, 64, 81, and 100, respectively. As seven squared is equal to 49, the square root of 49 is equal to seven.

In the same way, eight squared is equal to 64. The square root of 64 is equal to eight. 51 is greater than 49 but less than 64. Therefore, the square root of 51 must be greater than the square root of 49 and less than the square root of 64. We can, therefore, say that the square root of 51 is greater than seven but less than eight. The only arrow that lies between seven and eight is arrow 𝑐. This means that the arrow that represents the position of the square roots of 51 is 𝑐.

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