Chapter 10.4, Problem 7P

Solve each radical equation. Check your solution.

$\sqrt{5n-4}=6$

To determine

To find: the solution of the equation.

Answer to Problem 7P

The solution of the equation is $n=8$ .

Explanation of Solution

Given information:

The equation is $\sqrt{5n-4}=6$ .

Calculation: to find the solution of the equation, first square and then simplify,

  $\begin{array}{l}\sqrt{5n-4}=6\\ 5n-4=36\text{ [square]}\\ 5n=40\text{ [simplify]}\\ n=8\text{ [divide]}\end{array}$

Thus, the solution of the equation is $n=8$ .

To check the solution substitute $n=8$ , in the equation,

  $\begin{array}{l}\sqrt{5n-4}=6\\ \sqrt{5\left(8\right)-4}=6\text{ [substitute]}\\ \sqrt{36}=6\text{ [simplify]}\\ 6=6\end{array}$