To divide terms with radicals, divide the coefficients and radicands separately:

\( \frac{35\sqrt{6}}{7\sqrt{2}} \)
\( \frac{35}{7} \) \( \sqrt{\frac{6}{2}} \)
5 \( \sqrt{3} \)

To take the square root of a fraction, break the fraction into two separate roots then calculate the square root of the numerator and denominator separately:

\( \sqrt{\frac{64}{9}} \)
\( \frac{\sqrt{64}}{\sqrt{9}} \)
\( \frac{\sqrt{8^2}}{\sqrt{3^2}} \)
\( \frac{8}{3} \)
2\(\frac{2}{3}\)

By buying two shirts, Roger will save $33 x \( \frac{45}{100} \) = \( \frac{$33 x 45}{100} \) = \( \frac{$1485}{100} \) = $14.85 on the second shirt.

So, his total cost will be
$33.00 + ($33.00 - $14.85)
$33.00 + $18.15
$51.15

To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 300 meters to kilometers, divide the distance by 1000 to get 0.3km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.3km + 20.2km + 14.2km
total distance = 34.7km

To add these radicals together their radicands must be the same:

4\( \sqrt{175} \) + 2\( \sqrt{7} \)
4\( \sqrt{25 \times 7} \) + 2\( \sqrt{7} \)
4\( \sqrt{5^2 \times 7} \) + 2\( \sqrt{7} \)
(4)(5)\( \sqrt{7} \) + 2\( \sqrt{7} \)
20\( \sqrt{7} \) + 2\( \sqrt{7} \)

Now that the radicands are identical, you can add them together: