Jamelia estimates the square root of 72 in the following way: √72=2√36 = 2*6=12 Explain why her reasoning is incorrect. Estimate the square root of 72 to the nearest tenth without using your calculator. Show your work.

We are going to review the following procedure:

√72 = 2√36 = 2 * 6 = 12

The next step is incorrect:

√72 = 2√36

The correct step is:

√72 = √2 * (36).

Let's now calculate √72. We have the following steps:

Step 1:

√72 = √ (2 * (36))

Step 2:

√72 = √ (2 * (6) ^ 2)

Step 3:

√72 = 6√2

Step 4:

√72 = 6 * 1.41

Step 5:

√72 = 8.46

Step 6:

√72 = 8.5

Answer:

√72 = 8.5