Chapter 7.4, Problem 85PFA

To determine

To find the expression not equivalent to the given function

Answer to Problem 85PFA

  $v=2\sqrt{4h}$

Explanation of Solution

Given:

Function: $v=\sqrt{64h}$

Calculation:

Simplify the given options so that the expression not equivalent to $v=\sqrt{64h}$ can be found out.

Consider the first option,

  $\begin{array}{l}\Rightarrow v=2\sqrt{4h}\\ \Rightarrow v=\sqrt{4\times 4h}\\ \Rightarrow v=\sqrt{16h}\end{array}$

Consider the second option,

  $\begin{array}{l}\Rightarrow v=2\sqrt{16h}\\ \Rightarrow v=\sqrt{4\times 16h}\\ \Rightarrow v=\sqrt{64h}\end{array}$

Consider the third option,

  $\begin{array}{l}\Rightarrow v=2\cdot 2\sqrt{4h}\\ \Rightarrow v=2\cdot \sqrt{4\times 4h}\\ \Rightarrow v=2\cdot \sqrt{16h}\\ \Rightarrow v=\sqrt{4\times 16h}\\ \Rightarrow v=\sqrt{64h}\end{array}$

Consider the fourth option,

  $\begin{array}{l}\Rightarrow v=8\sqrt{h}\\ \Rightarrow v=\sqrt{64h}\end{array}$

Conclusion:

Therefore, the correct option is $v=2\sqrt{4h}.$