Final answer:
To approximate the location of the given numbers on a number line, find their square roots and round to the nearest decimal places. Approximations for the given numbers are: sqrt(144) = 12, sqrt[3]{1000} = 10, sqrt(130) ≈ 11.40, sqrt(110) ≈ 10.49, sqrt(120) ≈ 10.95, sqrt(115) ≈ 10.72, sqrt(133) ≈ 11.53.
Step-by-step explanation:
To approximate the location of the given numbers on a number line, we can use a calculator or computer. Let's start with the first number, square root of 144 (sqrt(144)). Taking the square root of 144 gives us 12. So, we can approximate the location of sqrt(144) as 12 on the number line. Following the same process for the remaining numbers:
- sqrt[3]{1000} is approximately 10, because 10^3 equals 1000.
- sqrt(130) is approximately 11.40, because the square root of 121 is 11, and 130 is closer to 121 than 144.
- sqrt(110) is approximately 10.49, because the square root of 100 is 10, and 110 is closer to 100 than 121.
- sqrt(120) is approximately 10.95, because the square root of 121 is 11, and 120 is closer to 121 than 100.
- sqrt(115) is approximately 10.72, because the square root of 100 is 10, and 115 is closer to 100 than 121.
- sqrt(133) is approximately 11.53, because the square root of 121 is 11, and 133 is closer to 121 than 144.
You can represent these approximations on a number line by labeling the respective positions with the approximated values.