Solving Equations with radical Exponents

Question

The question is $22= 2 + 5(5m - 11)^{1/2}$ so to try to solve this I first subtracted 2 and than divided by 5. than you get $4 = (5 m - 11)^{1/2}$

$$4 = \sqrt{5 m -11}$$

so$$16= 5m -11$$ or $$16+11=5m$$ or $$27 = 5 m$$ This cannot work

Answer 1

Notice, for $\sqrt{5m-11}$ to be defined we have $$5m-11\ge0\iff m\color{blue}{\geq \frac{11}{5}}$$

Now, we have $$4=\sqrt{5m-11}$$ Squaring both the sides $$4^2=(5m-11)$$ $$5m=11+16=27$$ $$m=\color{red}{\frac{27}{5}}$$

The above $m=\color{red}{\frac{27}{5}}\geq \color{blue}{\frac{11}{5}}$ Hence, your answer is correct.