Question

Use absolute value to simplify. You may need to factor first. $\sqrt{9 a^{2}+12 a b+4 b^{2}}$

Name: Problem 65, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2022-09-27T03:24:36-08:00
Duration: 58 s
Channel: Erika Bustos
Description: Use absolute value to simplify. You may need to factor first. √(9 a^2+12 a b+4 b^2)

   Use absolute value to simplify. You may need to factor first.
$\sqrt{9 a^{2}+12 a b+4 b^{2}}$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 65

Instant Answer

Solved by Expert Erika Bustos

09/27/2022

Step 1

We can factor it as follows: $9a^2 + 12ab + 4b^2 = (3a + 2b)^2$ Show more…

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Use absolute value to simplify. You may need to factor first. $\sqrt{9 a^{2}+12 a b+4 b^{2}}$

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Key Concepts

Factoring Perfect Square Trinomials

A perfect square trinomial is an expression that can be rewritten as the square of a binomial. Recognizing and factoring a trinomial like 9a² + 12ab + 4b² into (3a + 2b)² is a key technique that simplifies later steps in algebraic manipulation.

Square Roots and Absolute Values

When taking the square root of a squared expression, the result is the absolute value of the original expression because the square root function yields only the non-negative principal value. This ensures that ?(x²) equals |x|, accounting for both the positive and negative possibilities of x in the original squared term.

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