what am I doing wrong?

Question

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?

Answer 1

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).

Answer 2

the book says 6 - 2square root of 5

Answer 3

and when I did an online calculator, that's the answer it came up with as well

Answer 4

Mr. No Name is wrong. Definitely double-check with a calculator, as you did.

Answer 5

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 )