Question

Which number is farthest from 1 on the number line?
StartRoot 1.2 EndRoot
StartRoot 1.3 EndRoot
StartRoot 1.4 EndRoot
StartRoot 1.5 EndRoot

Answer 1

To determine which number is farthest from 1 on the number line, we can calculate the distance of each value from 1. The distance from a number \( x \) to 1 is given by \( |x - 1| \).

Now, we'll calculate each square root:

1. \( \sqrt{1.2} \approx 1.095 \)
2. \( \sqrt{1.3} \approx 1.140 \)
3. \( \sqrt{1.4} \approx 1.183 \)
4. \( \sqrt{1.5} \approx 1.225 \)

Next, we calculate the distance of each from 1:

1. Distance from \( \sqrt{1.2} \) is \( |1.095 - 1| = 0.095 \)
2. Distance from \( \sqrt{1.3} \) is \( |1.140 - 1| = 0.140 \)
3. Distance from \( \sqrt{1.4} \) is \( |1.183 - 1| = 0.183 \)
4. Distance from \( \sqrt{1.5} \) is \( |1.225 - 1| = 0.225 \)

Now we can compare these distances:

- \( 0.095 \) (from \( \sqrt{1.2} \))
- \( 0.140 \) (from \( \sqrt{1.3} \))
- \( 0.183 \) (from \( \sqrt{1.4} \))
- \( 0.225 \) (from \( \sqrt{1.5} \))

The largest distance is \( 0.225 \), which corresponds to \( \sqrt{1.5} \).

Therefore, the number that is farthest from 1 on the number line is \( \sqrt{1.5} \).