Question Video: Identifying the Position of Irrational Numbers on a Number Line Mathematics • 8th Grade

The positions of the numbers √120, √102, and √111 have been identified on the number line. By considering their size, decide which number is represented by 𝑎.

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Video Transcript

The positions of the numbers the square root of 120, the square root of 102, and the square root of 111 have been identified on the number line. By considering their size, decide which number is represented by 𝑎.

We’ve been given the square root of 120, the square root of 102, and the square root of 111. We don’t recognize any of these values as square numbers, which means the result will not be an integer. However, when we look on our number line, we do see two integer values; we see 10 and 11. And we know that 10 is equal to the square root of 100. 10 squared equals 100. And so, the square root of 100 equals 10. We can follow the same procedure to find what 11 would be. 11 is equal to the square root of 121. This is because 11 times 11 is 121. When we see the square root of 121, one of our values is the square root of 120. And the square root of 120 will be very close to the square root of 121 on a number line.

By that same reasoning, we know that the square root of 102 will be very near the square root of 100 on a number line. And we finally have the square root of 111, which falls about halfway between the square root of 100 and the square root of 121. Based on the data in the number line, we’re able to see that the square root of 102 would fall between 10 and 10.2. Our question was looking for the value that 𝑎 represented. And here, 𝑎 represents the square root of 102.

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