5under root xsquare +2x+3` ` ` ` ` ` `

Expert Answers

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You need to reduce the given expression to its lowest terms, hence, since the expression contains `x^2` under radical, hence, you need to use the following definition, such that:

`sqrt(x^2) = |x|`

Using the definition of absolute value, yields:

`|x| = +-x`

Hence, you will have to answers after the evaluation of expression, such that:

Considering `|x| = x` , yields:

`5sqrt(x^2) + 2x + 3 = 5x + 2x + 3 `

Adding the coefficients of terms that contain x yields:

`5sqrt(x^2) + 2x + 3 = 7x + 3`

Considering `|x| = -x` , yields:

`5sqrt(x^2) + 2x + 3 = -5x + 2x + 3 `

`5sqrt(x^2) + 2x + 3 =-3x + 3`

Hence, evaluating the expression, you will have two answers, such that: `5sqrt(x^2) + 2x + 3 = 7x + 3` for `x > 0` and `5sqrt(x^2) + 2x + 3 =-3x + 3` , for `x < 0` .

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