what am I doing wrong?
rational expression:
8/3 + square root of 5
I am multiplying both the numerator and denominator by the conjugate of (3 - square root of 5)
I get 8(3 - square root of 5)/3^2 - square root of 5^2
then I get 8(3 - square root of 5)/4
simplifies to 2(3 - square root of 5)
But apparently this is not the answer -- where have I gone wrong please?
You have not gone wrong. The answer you have is correct. The expression 8/3 + square root of 5 simplifies to 2(3 - square root of 5).
the book says 6 - 2square root of 5
and when I did an online calculator, that's the answer it came up with as well
Mr. No Name is wrong. Definitely double-check with a calculator, as you did.
Come one.
6 - 2 √5 is same as 2 ( 3 - √5 )
because
6 - 2 √5 = 2 ∙ 3 - 2 ∙ √5 = 2 ( 3 - √5 )
So:
8 / ( 3 + √5 ) = 6 - 2 √5 = 2 ( 3 - √5 )
To find what you are doing wrong, let's go step by step and analyze your approach.
Step 1: Multiply both the numerator and denominator by the conjugate of (3 - square root of 5).
In this step, you correctly identify the conjugate of (3 - square root of 5) as (3 + square root of 5).
Step 2: Apply the conjugate multiplication to the numerator and denominator.
In the numerator, you correctly distribute the 8. However, there is a mistake when multiplying the square root of 5 with the square root of 5. The result should be 5, not square root of 5 squared.
Let's correct this mistake and continue with the calculation:
Numerator:
8(3 - square root of 5) = 24 - 8(square root of 5)
Denominator:
(3^2) - (square root of 5)^2 = 9 - 5 = 4
Step 3: Simplify the expression.
Now, we can write the rational expression as (24 - 8(square root of 5))/4.
Step 4: Further simplify the expression.
To simplify further, we can divide the numerator and denominator by their greatest common divisor, which is 8 in this case.
(24/8 - 8(square root of 5)/8) / (4/8)
(3 - (square root of 5)) / 0.5
Finally, we can multiply both the numerator and denominator by 2 to get rid of the fraction in the denominator:
(2(3 - (square root of 5))) / 1
Therefore, the final simplified expression is:
2(3 - square root of 5).
You had the right idea, but made a small mistake in the multiplication of the numerator. By correcting that mistake and simplifying the expression correctly, the answer is indeed 2(3 - square root of 5).