Question

Calculate: √5/2-√5+2/2+√5

Answer 1

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

Answer 2

So,

$\frac{ \sqrt{5} }{2} - \sqrt{5} + \frac{2}{2} +\sqrt{5}$

$\frac{1}{2}\sqrt{5} - \sqrt{5} + \frac{2}{2} +\sqrt{5}$

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.

$\frac{1}{2}\sqrt{5} + \frac{2}{2}$

$\frac{1}{2}\sqrt{5} + 1$

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

$\sqrt{5}=2.23606797749978969640\ or\ approximately\ 2.236$

Substitute 2.236 for the square root of 5.

$\frac{1}{2}(2.236) + 1$

Multiply.
1.118 + 1

Add.
2.118

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