Express in simplest radical form
-9 square root 108 + square root 27
To simplify, we can factor the numbers under the square roots:
Starting with -9√108:
We can rewrite 108 as the product of its prime factors:
108 = 2 * 2 * 3 * 3 * 3
Now for simplifying the square root:
-9√(2 * 2 * 3 * 3 * 3)
-9 * 2 * 3 * √3
-54√3
Next, we simplify √27:
√27 = √(3 * 3 * 3)
3 * √3
Adding the two expressions together:
-54√3 + 3√3 = (-54 + 3)√3 = -51√3
The final simplified expression is -51√3.