are these correct?
Simplify.
1. 3 + sqrt8/ 2 - 2 sqrt8
simplified: - 8 * sqrt2 + 11 / 14
2. 4/ sqrt5 - sqrt3 - 4/ sqrt5 + sqrt3
simplified: 4 sqrt3
the first one looks good, but I can't parse the second.
You really need to use parentheses when typing rational expressions online.
2. (4/ sqrt5 - sqrt3) - (4/ sqrt5 + sqrt3)
simplified: 4 * sqrt3
still not good enough
you probably meant
4/(√5 - √3) - 4/(√5 + √3) , in that case form a common denominator ....
= ( 4(√5 + √3) - 4(√5 - √3) )/( (√5 + √3)(√5 - √3) )
= (4√5 + 4√3 - 4√5 + 4√3)/(5-9)
= 8√3/-4
= -2√3
check my arithmetic
maybe you mean
4/(sqrt5-sqrt 3) - 4/(sqrt5+sqrt3) ???
[4(sqrt 5 +sqrt 3) - 4(sqrt 5 -sqrt 3)]/(5-3)
(4/2) (2 sqrt 3)
4 sqrt 3
Ahhh confusing!!!
To check if the given simplifications are correct, we can simplify the expressions step by step and compare the results:
1. 3 + sqrt(8)/2 - 2sqrt(8)
To simplify this expression, we need to rationalize the denominators of the square roots.
sqrt(8) can be simplified as sqrt(4 * 2), which is equal to 2sqrt(2).
Applying this simplification to the expression, we get:
= 3 + (2sqrt(2)) / 2 - 2sqrt(8)
= 3 + sqrt(2) - 2(2sqrt(2))
= 3 + sqrt(2) - 4sqrt(2)
= 3 - 3sqrt(2)
So, the simplified expression is 3 - 3sqrt(2), which is different from the provided answer of -8sqrt(2) + 11/14. Therefore, the provided simplification is incorrect.
2. 4/sqrt(5) - sqrt(3) - 4/sqrt(5) + sqrt(3)
To simplify this expression, we can combine the like terms.
4/sqrt(5) - 4/sqrt(5) = 0
-sqrt(3) + sqrt(3) = 0
Therefore, all terms cancel out, and the simplified expression is 0.
So, the simplification 0 matches the provided answer of 4sqrt(3). Thus, the provided simplification is correct for the second expression.