Multiply both numerator and denominator by \(\displaystyle \sqrt{6}\):

\(\displaystyle \frac{3\sqrt{2}+2\sqrt{3}}{\sqrt{6}}\)

\(\displaystyle = \frac{(3\sqrt{2}+2\sqrt{3})\cdot \sqrt{6}}{\sqrt{6}\cdot \sqrt{6}}\)

\(\displaystyle = \frac{3\sqrt{2}\cdot \sqrt{6}+2\sqrt{3}\cdot \sqrt{6}}{6}\)

\(\displaystyle = \frac{3\sqrt{12} +2\sqrt{18} }{6}\)

\(\displaystyle = \frac{3\cdot \sqrt{4} \cdot \sqrt{3}+2\cdot \sqrt{9}\cdot \sqrt{2} }{6}\)

\(\displaystyle = \frac{3\cdot 2 \cdot \sqrt{3}+2\cdot3 \cdot \sqrt{2} }{6}\)

\(\displaystyle = \frac{6 \cdot \sqrt{3}+6 \cdot \sqrt{2} }{6}\)

\(\displaystyle = \sqrt{3}+ \sqrt{2}\)

The values are of the same power.  Divide the terms.

\(\displaystyle \frac{\sqrt{64}}{\sqrt{8}}= \sqrt{\frac{64}{8}}= \sqrt{8} = \sqrt{4}\times \sqrt{2}= 2\sqrt2\)

The correct answer is:   \(\displaystyle 2\sqrt2\)

The tab can be rounded to \(\displaystyle \$80\).  is equal to \(\displaystyle 0.20\).

\(\displaystyle =\frac{20}{100}=0.20\)

Now we can multiply the percent by the total amount.

\(\displaystyle 0.20 * 80 = 16\)

\(\displaystyle \$16\) is the most reasonable estimate of the recommended tip.

If \(\displaystyle 50,467\) is rounded to the nearest hundredth, the result will be \(\displaystyle 50,500\). 

Given that \(\displaystyle 505\cdot100=50,500\), the correct answer is \(\displaystyle 505\cdot100\)

437 rounded to the nearest hundred is 400.

877 rounded to the nearest hundred is 900.

551 rounded to the nearest hundred is 600.

Multiply the three whole multiples of 100 to get the desired estimate:

\(\displaystyle 437 \times 877 \times 551 \approx 400 \times 900 \times 600 = 216,000,000\)

\(\displaystyle 5 \frac{3}{7} < 5\frac{1}{2}\), so \(\displaystyle 5 \frac{3}{7}\)  rounded to the nearest unit is 5.

\(\displaystyle 9\frac{3}{5} \geq 9\frac{1}{2}\), so \(\displaystyle 9\frac{3}{5}\)  rounded to the nearest unit is 10.

\(\displaystyle 4\frac{4}{5} \geq 4\frac{1}{2}\), so \(\displaystyle 4\frac{4}{5}\)  rounded to the nearest unit is 5.

Multiply the three whole numbers to get the desired estimate:

\(\displaystyle 5 \frac{3}{7}\times 9\frac{3}{5} \times 4\frac{4}{5} \approx 5 \times 10 \times 5 = 250\)

8.19 rounded to the nearest unit is 8.

4.87 rounded to the nearest unit is 5

3.27 rounded to the nearest unit is 3.

7.42 rounded to the nearest unit is 7.

The desired estimate can be found as follows:

\(\displaystyle 8.19 \times 4.87 + 3.27 \times 7.42\)

\(\displaystyle \approx 8 \times 5 + 3 \times 7\)

\(\displaystyle =40 + 3 \times 7\)

\(\displaystyle =40 + 21 = 61\)

\(\displaystyle 8 \frac{2}{7} < 8\frac{1}{2}\), so \(\displaystyle 8 \frac{2}{7}\) rounded to the nearest unit is 8.

\(\displaystyle 9\frac{4}{5} \ge 9\frac{1}{2}\), so \(\displaystyle 9\frac{4}{5}\) rounded to the nearest unit is 10.

\(\displaystyle 3\frac{4}{5} \ge 3\frac{1}{2}\), so \(\displaystyle 3\frac{4}{5}\) rounded to the nearest unit is 4.

\(\displaystyle 6\frac{2}{5} < 6\frac{1}{2}\), so \(\displaystyle 6\frac{2}{5}\) rounded to the nearest unit is 6.

The desired estimate can be found as follows:

\(\displaystyle 8 \frac{2}{7}\times 9\frac{4}{5}+ 3\frac{4}{5} \times 6\frac{2}{5}\)

\(\displaystyle \approx 8 \times 10 + 4 \times 6\)

\(\displaystyle = 80 + 4 \times 6\)

\(\displaystyle = 80 + 24 = 104\)

Round each of the amounts to the nearest ten dollars as follows:

$187.54 rounds to $190.

$218.89 rounds to $220.

$174.74 rounds to $170.

$104.76 rounds to $100.

$189.75 rounds to $190.

$228.64 rounds to $230.

Add the rounded figures:

\(\displaystyle 190+220+170+100+190+230 = 1,100\)

8.39 rounded to the nearest unit is 8 because 0.39 is less than 0.5.

7.34 rounded to the nearest unit is 7 because 0.34 is less than 0.5.

3.52 rounded to the nearest unit is 4 because 0.52 is greater than 0.5.

Multiply the three whole numbers to get the desired estimate:

\(\displaystyle 8.39 \times 7.34 \times 3.52 \approx 8 \times 7 \times 4 = 56 \times 4 = 224\)