simplify the expression square root 45 + 2 square root 500

To simplify the expression squre root of 45+ 2square root
of 500.

Let E = sqrt45
+2sqrt500.

So we have find in the value of E  simple form.
We take term by term for simplification:

First term
sqrt45:

sqrt45 =
sqrt(9*5)

sqrt45 =
(sqrt9)(sqrt5)

sqrt45 =
3sqrt5.........................(1)

The second term
2sqrt500:

2 sqrt500 = 2*sqrt(100*5) = 2*(sqrt
100)(sqrt5)

2sqrt500 =
2*10sqrt5

 2sqrt100 =
20sqrt5...........(2).

From (1) and (2) we get the value of
E by addtion:

E = sqrt45 +2 sqrt500 =
3sqrt5+20sqrt5

sqrt45+2sqrt500 = 3sqr5+20
sqrt5.

sqrt45+2sqrt500 =
(3+20)sqrt5

sqrt45 +2sqrt500 =
23sqrt5.

Therefore the 23sqrt5 is the simple form of
sqrt45+2sqrt500.