# simplify the expression square root 45 + 2 square root 500

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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.

We will use the term sqrt to denote square root. Thus the given expression cab written as:

sqrt(45) + 2sqrt(500)

This can be simplified as follows:

= sqrt(9*5) + 2sqrt(100*5)

= sqrt(9)*sqrt(5) + 2sqrt(100)*sqrt(5)

= 3*sqrt(5) + 2*10*sqrt(5)

= 3*sqrt(5) + 20*sqrt(5)

= sqrt(5)(3 + 20)

= 23sqrt(5)

We have to simplify: square root 45 + 2 square root 500

Now we can write square root 45 + 2 square root 500 as

sqrt 45 + 2* sqrt 500

=> sqrt 9*5 + 2* sqrt 100*5

taking 9 and 100 out of the square roots as they are perfect squares.

=> 3 sqrt 5 + 2*10* sqrt 5

separating sqrt 5

=> sqrt 5 * ( 3 + 2*10)

=> sqrt 5 * ( 20 +3)

=> 23 * sqrt 5

**Therefore the required result is 23 * sqrt 5**