Question

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

Answer 1

Simplify:

$2\sqrt{27}+3\sqrt{48}$

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:

$\begin{gathered} 2\sqrt{9\cdot3}+3\sqrt{16\cdot3} \\ 2\sqrt{9}\sqrt{3}+3\sqrt{16}\sqrt{3} \\ 2\cdot3\sqrt{3}+3\cdot4\sqrt{3} \\ 6\sqrt{3}+12\sqrt{3} \end{gathered}$

Now we can simplify because both expressions are similar:

$18\sqrt{3}$