simplify the sum or difference: -6sqrt10 + 5sqrt90
-6sqrt10 + 5sqrt90 can be simplified as follows:
-6sqrt10 + 5sqrt(10 x 9 x 1) (since 90 = 10 x 9)
-6sqrt10 + 5sqrt10sqrt9sqrt1 (using the product rule of square roots)
-6sqrt10 + 5 x 3 x sqrt10 (since sqrt9 = 3 and sqrt1 = 1)
-6sqrt10 + 15sqrt10
= 9sqrt10
Therefore, -6sqrt10 + 5sqrt90 simplifies to 9sqrt10.
To simplify the given expression, -6√10 + 5√90, we can first simplify the square roots.
√10 = √(2 * 5) = √2 * √5 = √2 * √5 = √2√5 = √10
√90 = √(9 * 10) = 3√10
Now we substitute these values back into the expression:
-6√10 + 5√90 = -6√10 + 5(3√10)
= -6√10 + 15√10
Next, we combine like terms:
= (-6 + 15)√10
= 9√10
So, the simplified form of -6√10 + 5√90 is 9√10.
To simplify the sum or difference: -6√10 + 5√90, we first need to simplify the square roots.
We can start by simplifying the square roots under the radical signs.
√10 can't be simplified any further because 10 does not have any perfect square factors.
√90 can be simplified to √(9 × 10). Since 9 is a perfect square (3^2) and doesn't have any square factors other than 1, we can move the 3 outside of the radical sign: 3√10.
Now, let's rewrite the expression with the simplified square roots:
-6√10 + 5√90
= -6√10 + 5(3√10)
Now we can combine like terms. Since both terms have √10, we can add the coefficients:
-6√10 + 5(3√10) = -6√10 + 15√10
Again, combining like terms, we have:
-6√10 + 15√10 = (15 - 6)√10
Finally, we simplify the coefficients:
(15 - 6)√10 = 9√10
Therefore, the simplified form of -6√10 + 5√90 is 9√10.