-6 square root 10 + 5 square root 90
-6√10 + 5√90
To simplify this expression, we can first break down the square roots into their prime factors:
√10 = √(2 * 5) = √2 * √5 = √2 * √5 = √2 * 2√5 = 2√5
√90 = √(2 * 3^2 * 5) = √2 * √(3^2) * √5 = 3√2 * 3 * √5 = 3√2 * 3√5 = 9√10
Now we can substitute these back into our original expression:
-6√10 + 5√90
= -6(2√5) + 5(9√10)
= -12√5 + 45√10
Therefore, the simplified form of the expression is:
-12√5 + 45√10