The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).

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

2\( \sqrt{12} \) + 6\( \sqrt{3} \)
2\( \sqrt{4 \times 3} \) + 6\( \sqrt{3} \)
2\( \sqrt{2^2 \times 3} \) + 6\( \sqrt{3} \)
(2)(2)\( \sqrt{3} \) + 6\( \sqrt{3} \)
4\( \sqrt{3} \) + 6\( \sqrt{3} \)

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

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 500 meters to kilometers, divide the distance by 1000 to get 0.5km then add the remaining distances:

total distance = swim + bike + run
total distance = 0.5km + 50.6km + 8.100000000000001km
total distance = 59.2km

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To add or subtract terms with exponents, both the base and the exponent must be the same. In this case they are so add the coefficients and retain the base and exponent:

2a² + 5a²
(2 + 5)a²
7a²