Question

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative. $\sqrt{x^{2}+4 x+4}$

Name: Problem 71, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2021-04-14T12:23:48-08:00
Duration: 17 s
Channel: Erika Bustos
Description: Simplify. Assume that all variables represent positive values and that the radicand is nonnegative. √(x^2+4 x+4)

   Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{x^{2}+4 x+4}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 71

Instant Answer

Solved by Expert Erika Bustos

04/14/2021

Step 1

In this case, we have $x^2 + 4x + 4$, which is a quadratic expression. Show more…

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Simplify. Assume that all variables represent positive values and that the radicand is nonnegative. $\sqrt{x^{2}+4 x+4}$

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Key Concepts

Variable Domain Considerations in Radical Simplification

When simplifying expressions involving radicals, it is important to consider the domain restrictions of the variables involved. If variables are positive and the expression inside the radical is nonnegative, it permits the removal of absolute value signs, leading to a direct simplification of the expression.

Perfect Square Trinomial

A perfect square trinomial is an expression that can be factored into the square of a binomial. Recognizing such patterns in algebra allows for simpler manipulation and reduction of quadratic expressions, which is particularly useful under a radical.

Square Root of a Squared Expression

The property that the square root of a square is equal to the absolute value of the original expression is fundamental in algebra. This concept is crucial when simplifying radicals since it directs whether or not an absolute value sign must be retained based on variable conditions.

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