Question

For what values of $x$ will $\sqrt{(x+3)^{2}}=x+3$ ? Explain how you determined your answer.

Name: Problem 114, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2022-02-25T18:24:24-08:00
Duration: 40 s
Channel: Vivek Kumar
Description: For what values of x will √((x+3)^2)=x+3 ? Explain how you determined your answer.

   For what values of $x$ will $\sqrt{(x+3)^{2}}=x+3$ ? Explain how you determined your answer.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 114

Instant Answer

Solved by Expert Vivek Kumar

02/25/2022

Step 1

2) If $x+3 < 0$, then $|\,(x+3)| = -(x+3)$, so we have: $-(x+3) = x+3$ Solving this equation, we get: $-x-3 = x+3$ $-6 = 2x$ $x = -3$ However, this value of $x$ does not satisfy the condition $x+3 < 0$, so there are no solutions in this case. Show more…

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For what values of $x$ will $\sqrt{(x+3)^{2}}=x+3$ ? Explain how you determined your answer.

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Key Concepts

Domain Restrictions

Domain restrictions are conditions on the variables that ensure expressions or equations are mathematically valid. In this context, the equation ?((x+3)²) = x+3 holds true only when the inner expression, x+3, is non-negative, leading to the restriction that x must be greater than or equal to -3.

Square Root Function

The square root function is defined to return the non-negative root of a non-negative number. Thus, when applied to a squared expression, it yields the absolute value of that expression, ensuring only non-negative outputs are considered.

Absolute Value

The absolute value of a real number is its non-negative magnitude from zero on the number line. In expressions like ?((x+3)²), taking the square root of a square results in the absolute value of the expression inside the square, making it |x+3|.

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