Chapter 6.3, Problem 16OE

To determine

Is the expression $\sqrt{x}+\sqrt{x}$ is equivalent to $\sqrt{2x}$ . Explain.

Answer to Problem 16OE

No, the expression is not true.

Explanation of Solution

Given information: The given expression is,

  $\sqrt{x}+\sqrt{x}=\sqrt{2x}\mathrm{......}\left(1\right)$

Calculation: Simplify left hand side of (1),

  $\begin{array}{c}\sqrt{x}+\sqrt{x}=\left(1+1\right)\sqrt{x}\\ =2\sqrt{x}\mathrm{....}\left(\begin{array}{l}\text{which is not }\\ \text{equal to}\sqrt{2x}\end{array}\right)\end{array}$

Now, the simplified left hand side of (1) is not equal to right side of (1). Therefore, the given expression $\sqrt{x}+\sqrt{x}$ is not equivalent to $\sqrt{2x}$ .