Add 2-√8+3-√8 .(1 point)
2-√8+3-√8 = (2+3) - (√8+√8) = 5 - 2√8 = 5 - 2(2√2) = 5 - 4√2
To add the given expression, 2 - √8 + 3 - √8, you first need to simplify the square root of 8 (√8).
Step 1: Simplify √8
The square root of 8 can be simplified by factoring out the perfect square number, if one exists. In this case, 4 is the largest perfect square that divides evenly into 8.
√8 = √(4 * 2) = √4 * √2 = 2√2
Now that we have simplified the square root of 8, let's substitute it back into the original expression.
2 - 2√2 + 3 - 2√2
Step 2: Combine like terms
Combine the coefficients of the terms without the square root term, and also combine the coefficients of the terms with the square root term.
(2 + 3) + (-2√2 - 2√2) = 5 - 4√2
So, the simplified expression is 5 - 4√2.
To add 2-√8+3-√8, we first combine the like terms.
The like terms in this expression are the numbers 2 and 3, and the terms with the square root of 8: -√8 and -√8.
Adding the numbers 2 and 3, we get 5.
Adding the terms with the square root of 8, we can simplify them. Since they have the same radical term (√8), we can combine them.
-√8 + (-√8) = -2√8.
Now, we can rewrite the expression: 2-√8+3-√8 = 5 - 2√8.
So, the simplified expression is 5 - 2√8.