Question

Simplify. Assume that all variables represent positive values and that the radicand is nonnegative. $\sqrt{9 a^{2}-6 a+1}$

Name: Problem 72, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2022-04-04T21:33:38-08:00
Duration: 41 s
Channel: James Kiss
Description: Simplify. Assume that all variables represent positive values and that the radicand is nonnegative. √(9 a^2-6 a+1)

   Simplify. Assume that all variables represent positive values and that the radicand is nonnegative.
$\sqrt{9 a^{2}-6 a+1}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 72

Instant Answer

Solved by Expert James Kiss

04/04/2022

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We have $9a^2 - 6a + 1$. This looks like a quadratic expression. Show more…

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Simplify. Assume that all variables represent positive values and that the radicand is nonnegative. $\sqrt{9 a^{2}-6 a+1}$

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Key Concepts

Perfect Square Trinomial

A perfect square trinomial is a specific type of polynomial that can be factored into the square of a binomial. Identifying such a pattern, like rewriting 9a² - 6a + 1 as (3a - 1)², simplifies the expression by reducing complex polynomials to simpler squared terms.

Square Root of a Square

Taking the square root of a squared expression involves the absolute value of the original expression. Generally, ?(x²) equals |x| to ensure that the result is nonnegative, which is essential in algebra when dealing with square roots and maintaining correct simplification of expressions.

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