Question

Calculate:
√5/2-√5+2/2+√5

Answer 1

So,


`( √(5) )/(2) - √(5) + (2)/(2) +√(5)`


`(1)/(2)√(5) - √(5) + (2)/(2) +√(5)`

First, we have to simplify the expression.

We can see that there is a negative square root of 5 and a positive square root of 5. They cancel out. In addition, we know that two-halves are equal to 1.


`(1)/(2)√(5) + (2)/(2)`


`(1)/(2)√(5) + 1`

Since the square root of 5 can be thought of as 5 to the one-half power, we should evaluate that first.


`√(5)=2.23606797749978969640\ or\ approximately\ 2.236`

Substitute 2.236 for the square root of 5.


`(1)/(2)(2.236) + 1`

Multiply.
1.118 + 1

Add.
2.118

So the expression is approximately equal to 2.118 (exactly 2.1180339887498948482045868343656).

Answer 2

-√5/2+√5+1
-√5/2+2√5/2+1
√5/2+1
(√5+2)/2