Jaclyn estimates the square root of 50 in the following way:

/sqrt (50) = 2/sqrt (25) = 2=10

(a) Explain why her reasoning is incorrect.

(b) Estimate the square root of 50 to the nearest tenth without using your calculator.

Show your work.

Answer:

The square root of 50 is 5/sqrt (2).

To get the square root of a number, first find its factors which have squares. In this case of 50, the factors which have a square is 25 x 2. Since 25 is a perfect square, you can get its square root which is 5 and put it outside the radical sign, leaving only the number 2. Which doesnt have a perfect square as its factor.

Therefore the final answer is 5/sqrt (2).