Final answer:
The expression √40 - √90 + √250 simplifies to 4√10 by factoring each number under the square root, isolating square numbers, and then combining like terms.
Step-by-step explanation:
To find the exact value of the expression √40 - √90 + √250, we need to simplify each square root separately. Each number under the square root can be factored into a product of square numbers and non-square numbers, which allows us to simplify the square roots.
Let's start with √40. The number 40 can be factored into 4 x 10, where 4 is a square number. Therefore, √40 = √(4⋅ 10) = √4⋅√10 = 2√10.
Next, √90 can be simplified by recognizing that 90 = 9 x 10, where 9 is a square number. So, √90 = √(9⋅ 10) = √9⋅√10 = 3√10.
Lastly, √250 can be factored into 25 x 10, and 25 is a square number. Thus, √250 = √(25⋅ 10) = √25⋅√10 = 5√10.
Combining all the simplified square roots, we get the expression 2√10 - 3√10 + 5√10. We can combine like terms since each term contains the √10 factor. This results in:
(2 - 3 + 5)√10 = 4√10
Therefore, the exact value of the expression √40 - √90 + √250 is 4√10.