Question

use a calculator to approximate the following square root to the nearest thousandth.
a. $sqrt{24} + sqrt{216} =$
b. $sqrt{240} =$
c. $2sqrt{6} + 6sqrt{6} =$
d. $8sqrt{6} =$
question help: ebook message instructor

Explanation:

Step1: Calculate $\sqrt{24}$ and $\sqrt{216}$

$\sqrt{24} \approx 4.89898$, $\sqrt{216} \approx 14.69694$

Step2: Sum the two approximations

$4.89898 + 14.69694 = 19.59592$

Step3: Round to nearest thousandth

$19.59592 \approx 19.596$

Step4: Calculate $\sqrt{240}$

$\sqrt{240} \approx 15.49193$

Step5: Round to nearest thousandth

$15.49193 \approx 15.492$

Step6: Combine like radical terms

$2\sqrt{6} + 6\sqrt{6} = (2+6)\sqrt{6} = 8\sqrt{6}$

Step7: Calculate $8\sqrt{6}$

$\sqrt{6} \approx 2.44949$, $8 \times 2.44949 = 19.59592$

Step8: Round to nearest thousandth

$19.59592 \approx 19.596$

Step9: Calculate $8\sqrt{6}$ (repeat for clarity)

$\sqrt{6} \approx 2.44949$, $8 \times 2.44949 = 19.59592$

Step10: Round to nearest thousandth

$19.59592 \approx 19.596$

Answer:

a. $19.596$
b. $15.492$
c. $19.596$
d. $19.596$