1) Estimate the square root of 40 using the number line below
So you know 40 is between the two perfect square numbers 36 and 49. 40 is closer to 36 so you put 40 before the half way point. You know that that 40 can't be more than 7 because the square root of 49 is 7 and 40 is less than 7. So the number for 40 should be 6 decimal something. The number after the decimal should be less than 5 because the half way point is 6.5. So lets make is 6.4!
b) Estimate the whole number that has a square root two thirds of the way along the number line between 3 and 4.
The square root of 9 is 3 and the square root of 16 is 4. We have to find 1/3 of the way along the number line, which s 14.
4) Identify all of the whole numbers with a square root larger than 5 and smaller than 6.
The square root of 5 of 25 so the numbers have to be larger than 25. The square root of 6 is 36 so the numbers have to be smaller than 36.
6) Write the perfect square immediately before and after the whole number, and then estimate the square root of the whole number to one decimal place. Check your estimates with a calculator.