Question

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.

Answer 1

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