Answer:
6√6 - 5√2 + 2.
Explanation:
AI-generated answer
To solve the expression 2√54 - 5√2 + √16, we can simplify each term individually and then combine them.
First, let's simplify each term:
√54 can be simplified as √(9 * 6). Since 9 is a perfect square, we can take its square root as 3. Therefore, √54 = 3√6.
√2 cannot be simplified further, so we keep it as it is.
√16 can be simplified as √(4 * 4). Since 4 is a perfect square, we can take its square root as 2. Therefore, √16 = 2.
Now, let's substitute these simplified terms back into the original expression:
2√54 - 5√2 + √16
= 2(3√6) - 5√2 + 2
Next, we can simplify the expression further by multiplying the coefficients (numbers in front of the square roots) with the simplified square roots:
= 6√6 - 5√2 + 2
So, the simplified expression is 6√6 - 5√2 + 2.
Note that this is the final answer and cannot be simplified further.