Question

Ross is comparing square root 11 and 5.4 repeating. he says that square root 11 is greater than 5.4 repeating because square root equals 5.5. What is the correct comparison?

Answer 1

The correct comparison is that the square root of 11 is greater than 5.4 repeating due to the sqare root of 11 being approximately 3.32 while 5.4 repeating is approximately 5.44.

Step-by-step explanation:

The correct comparison is that the square root of 11 is greater than 5.4 repeating. Although Ross says that the square root of 11 equals 5.5, it is not entirely accurate. Let's evaluate both numbers to see the correct comparison:

Square root of 11:

To find the square root of 11, we can use a calculator or estimate it. The square root of 11 is approximately 3.31662479 (rounded to 8 decimal places), which is greater than 5.5.

5.4 repeating:

To represent 5.4 repeating as a fraction, we can use a trick. Let x = 5.4 repeating. Multiply both sides of the equation by 10 to get 10x = 54.4 repeating. Subtracting the two equations, we get 10x - x = 54.4 repeating - 5.4 repeating, which simplifies to 9x = 49, and x = 49/9 = 5.44444 repeating. Therefore, 5.4 repeating is less than the square root of 11.