Question

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

Name: Problem 73, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2021-04-14T12:21:20-08:00
Duration: 32 s
Channel: Erika Bustos
Description: Simplify. Assume that all variables represent positive values and that the radicand is nonnegative. √(4 x^2+4 x y+y^2)

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

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 73

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Solved by Expert Erika Bustos

04/14/2021

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$\sqrt{4(x^2 + xy + y^2)}$ Show more…

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

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Key Concepts

Domain Considerations

Considering domain restrictions is essential when simplifying radical expressions because the definition of the square root function relies on nonnegative inputs. When variables are known to represent positive values, the absolute value in the simplified expression can be removed, resulting in a direct linear expression.

Simplification of Radical Expressions

This concept involves reducing expressions under a radical sign by recognizing when the radicand is a perfect square. The square root of a square can be simplified to the absolute value of the original expression, as long as the conditions on the variables ensure nonnegativity.

Perfect Square Trinomial

A perfect square trinomial is a quadratic expression that can be factored into the square of a binomial. Recognizing the pattern a^2 + 2ab + b^2 helps in rewriting the expression as (a+b)^2, which is key to simplifying the square root of the expression.

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