### 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.