Question

Use absolute value to simplify. You may need to factor first. $\sqrt{a^{2}-8 a+16}$

Name: Problem 63, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2022-09-25T03:28:25-08:00
Duration: 1 min 2 s
Channel: Erika Bustos
Description: Use absolute value to simplify. You may need to factor first. √(a^2-8 a+16)

   Use absolute value to simplify. You may need to factor first.
$\sqrt{a^{2}-8 a+16}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 63

Instant Answer

Solved by Expert Erika Bustos

09/25/2022

Step 1

We notice that $a^2 - 8a + 16$ is a perfect square trinomial, which can be factored as $(a - 4)^2$. Show more…

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Use absolute value to simplify. You may need to factor first. $\sqrt{a^{2}-8 a+16}$

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Key Concepts

Perfect Square Trinomials

A perfect square trinomial is a quadratic expression that can be written as the square of a binomial. Recognizing this pattern allows the expression to be factored into a form like (x – c)², which is particularly helpful when simplifying square roots.

Square Roots and Absolute Value

The property that the square root of a squared quantity is the absolute value of the original expression (i.e., ?(x²) = |x|) is fundamental. This ensures that the result is non-negative, aligning with the definition of a square root in real numbers.

Factoring Quadratic Expressions

Factoring quadratic expressions is a technique used to rewrite a quadratic polynomial into a product of simpler binomial factors. This process simplifies the expression, making subsequent operations, such as taking square roots or solving equations, more straightforward.

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