add then simplify.by collecting like radical terms if possible assuming that all expressions under radicals represent non negative numbers:

√5a + 2√45a^3

Suppose that the volumes of four stars in the Milky Way are 2.7 × 1018 km3, 6.9 × 1012 km3, 2.2 × 1012 km3, and 4.9 × 1021 km3. What is the order of the stars from least to greatest volume?

To add and simplify the expression √5a + 2√45a^3, we need to follow these steps:

Step 1: Simplify the square roots.
- The square root of 5a cannot be simplified any further.
- The square root of 45a^3 can be simplified by factoring out the perfect square: the largest perfect square that divides evenly into 45a^3 is 9a^2.
√45a^3 = √(9a^2 * 5a) = 3a√5a

Now, we have: √5a + 2(3a√5a)

Step 2: Collect the like radical terms.
Since both terms have a radical of √5a, we can combine them by adding their coefficients.
√5a + 2(3a√5a) = √5a + 6a√5a

Step 3: Simplify the coefficients.
To simplify the coefficients, we can factor out the common factor of √5a:
√5a + 6a√5a = (√5a)(1 + 6a)

So, the simplified expression is (√5a)(1 + 6a).