Final answer:
The square root of 29 is between 5 and 6 but less than 5.7145. On a number line, √29 would be plotted to the left of 5.7145, both numbers falling between 5 and 6.
Step-by-step explanation:
To compare √29 and 5.7145…, first, note that √29 is the square root of 29. Since 5² = 25 and 6² = 36, we can conclude that √29 is between 5 and 6. To get more precise, √25 = 5, and 29 - 25 = 4, so √29 will be somewhat more than 5. Since 5.7145… is more than 5.5 but less than 5.8, it's also between 5 and 6. However, without calculating √29 exactly, we know it is less than 5.7145… because 5.7145² would be over 32, higher than 29.
To plot these numbers on a number line, we would place a mark for √29 between 5 and 5.7145…, and then another mark for 5.7145…, which will be further to the right but still between 5 and 6.
To compare √29 and 5.7145... we need to find their approximate values and plot them on a number line.
√29 is the square root of 29. Since 5^2 = 25 and 6^2 = 36, we know that the square root of 29 is between 5 and 6. By estimating, we can say that √29 is approximately 5.4.
5.7145... is a decimal number. It is closer to 6 than to any other whole number, so we can say that 5.7145... is approximately 6.
Plotting these numbers on a number line, we would place √29 at approximately 5.4 and 5.7145... at approximately 6.