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

√75=3√25=3 * 5=15

Explain why her reasoning is incorrect.

Estimate the square root of 75 to the nearest thousandths without using your calculator. Show your work.

Note: If you use a calculator you will get the wrong answer.

Approximately 8.65

Step-by-step explanation:

The error in the procedure occurred when Jacob put the value of 3 outside the square root. This value should be inside a square root as well, like this:

√75 = √3 * √25

Then, with the equation above, we can estimate the value of √75 knowing that √3 is approximately 1.73:

√75 = √3 * √25 = √75 = √3 * 5 = √75 ≈ 1.73 * 5 ≈ 8.65