Answer:
Explanation:
To simplify the expression 7√24 + √90 - 8√54 completely, you can simplify each square root separately and then combine like terms:
1. Simplify √24:
√24 = √(4 * 6) = 2√6
2. Simplify √90:
√90 = √(9 * 10) = 3√10
3. Simplify √54:
√54 = √(9 * 6) = 3√6
Now, substitute these simplified values back into the original expression:
7(2√6) + 3√10 - 8(3√6)
Now, distribute the coefficients:
14√6 + 3√10 - 24√6
Next, combine like terms by adding or subtracting the square root terms with the same radicand (the number inside the square root symbol):
(14√6 - 24√6) + 3√10
Combine the √6 terms:
-10√6 + 3√10
So, the completely simplified expression is:
-10√6 + 3√10