Question

Simplify each expression. $-\sqrt{x^{2}-10 x+25}$

   Simplify each expression.
$-\sqrt{x^{2}-10 x+25}$

Intermediate Algebra for College Students

Intermediate Algebra for College Students

Robert Blitzer 7th Edition

Chapter 7, Problem 46

Instant Answer

Solved by Expert Amy Jiang

06/06/2020

Step 1

$x^2 - 10x + 25 = (x - 5)^2$ Show more…

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Simplify each expression. $-\sqrt{x^{2}-10 x+25}$

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Key Concepts

Perfect Square Trinomial

A perfect square trinomial is a quadratic expression that can be factored into a binomial squared. Recognizing that expressions come in the form a² - 2ab + b², which factors as (a - b)², is crucial for simplifying complex expressions and radicals.

Square Root and Absolute Value Relationship

When taking the square root of a squared expression, the result is the absolute value of the original expression, not simply the expression itself. In algebra, sqrt(y²) equals |y|, ensuring that the outcome is nonnegative, which aligns with the definition of a square root.

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