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Chapter 9: Problem 14

Write the proper restrictions that must be placed on the variable so that each expression represents a real number. $$ \sqrt{x+5} $$

Short Answer

Expert verified
Answer: The domain of the square root expression $$\sqrt{x+5}$$ is $$x \geq -5$$. This means the expression represents a real number for every x value greater than or equal to -5.

Step by step solution

01

Rewrite the inequality

To find the restrictions on the variable x, we first need to rewrite the inequality involving the expression inside the square root: $$ x + 5 \geq 0 $$
02

Solve the inequality

In this step, we will solve the inequality by isolating x: \begin{align*} x + 5 &\geq 0 \\ x &\geq -5 \end{align*}
03

Write the restrictions of the variable x

The inequality we found tells us the proper restrictions on the variable x for the expression to represent a real number: $$ x \geq -5 $$ The expression $$\sqrt{x+5}$$ represents a real number for every x value greater than or equal to -5.

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Most popular questions from this chapter

For the following problems, simplify each of the square root expressions. $$ (\sqrt{10}-\sqrt{3})(\sqrt{5}+\sqrt{2}) $$

For the following problems, solve the equations. $$ \sqrt{a^{2}+5}+5=a $$

Simplify each expression by performing the indicated operation. $$ (2-\sqrt{6})^{2} $$

Simplify \(\frac{1}{2+\sqrt{x}}\) by rationalizing the denominator.

For the following problems, simplify the expressions. $$ \sqrt{18 x^{2} y} \sqrt{2 x^{2} y} $$
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