Chapter 6.7, Problem 14CYU

To determine

Solve the equation ${\left(2y+6\right)}^{\frac{1}{4}}-2=0$ for the value of $\left(y\right)$ .

Answer to Problem 14CYU

The value of $\left(y\right)$ is equal to $5$ which best fits to option B.

Explanation of Solution

Given information: The given equation is,

  ${\left(2y+6\right)}^{\frac{1}{4}}-2=\mathrm{0......}\left(1\right)$

Calculation: The value of $\left(y\right)$ from (1) can be evaluated as,

  $\begin{array}{c}{\left(2y+6\right)}^{\frac{1}{4}}-2=\mathrm{0....}\left(\text{Given}\right)\\ {\left(2y+6\right)}^{\frac{1}{4}}=2\\ {\left({\left(2y+6\right)}^{\frac{1}{4}}\right)}^4={\left(2\right)}^4\\ 2y+6=16\\ y=5\end{array}$