Simplify 13 square root of 27 will it be 16 power route of 339 power route of three or just 39 or this radical expression is already fully simplified

1 answer

To simplify \( 13 \sqrt{27} \), we first simplify \( \sqrt{27} \).

The number \( 27 \) can be factored as:

\[ 27 = 9 \times 3 = 3^2 \times 3 \]

Thus, we can simplify \( \sqrt{27} \):

\[ \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3 \sqrt{3} \]

Now, substituting this back into the expression \( 13 \sqrt{27} \):

\[ 13 \sqrt{27} = 13 \times 3 \sqrt{3} = 39 \sqrt{3} \]

So, \( 13 \sqrt{27} \) simplifies to \( 39 \sqrt{3} \).

Therefore, the expression \( 39 \sqrt{3} \) is the simplified form, and it is not equal to \( 16 \sqrt{339} \) or any other expression provided.

In conclusion, the simplified expression is:

\[ 39 \sqrt{3} \]