Math Snap

STEP 1

1. We need to approximate the square root of $72$.
2. The approximation should be rounded to the nearest thousandth.

STEP 2

1. Use a calculator to find the square root.
2. Round the result to the nearest thousandth.
3. Verify the approximation is reasonable.

STEP 3

Use a calculator to find $\sqrt{72}$.

STEP 4

The calculator gives $\sqrt{72} \approx 8.485281374$.

STEP 5

Round $8.485281374$ to the nearest thousandth.
$$8.485281374 \approx 8.485$$

Verify the approximation by squaring $8.485$ to check if it is close to $72$.
$$8.485^2 \approx 71.995225$$ Since $71.995225$ is close to $72$, the approximation is reasonable.
The approximation of $\sqrt{72}$ rounded to the nearest thousandth is:
$$\boxed{8.485}$$