Question

How do you rewrite 2√27 + 3√48 into simplified radical form?

Answer 1

Simplify:

`2√(27)+3√(48)`

These expressions cannot be added because the radicands are different (27 and 48).

We can rewrite the radicands as follows:

27 = 9 x 3

48 = 16 x 3

Both 9 and 16 are perfect squares, so the simplification is possible:

`\begin{gathered} 2√(9\cdot3)+3√(16\cdot3) \\ 2√(9)√(3)+3√(16)√(3) \\ 2\cdot3√(3)+3\cdot4√(3) \\ 6√(3)+12√(3) \end{gathered}`

Now we can simplify because both expressions are similar:

`18√(3)`