Question

question 5
solve the equation \\(\sqrt{6n - 5} + 1 = 8\\)

Explanation:

Step1: Isolate the square root term

Subtract 1 from both sides of the equation $\sqrt{6n - 5}+1 = 8$. So we get $\sqrt{6n - 5}=8 - 1=7$.

Step2: Eliminate the square root

Square both sides of the equation $\sqrt{6n - 5}=7$. We have $(\sqrt{6n - 5})^2 = 7^2$, which simplifies to $6n - 5 = 49$.

Step3: Solve for n

Add 5 to both sides: $6n=49 + 5=54$. Then divide both sides by 6: $n=\frac{54}{6}=9$.

Step4: Check the solution

Substitute $n = 9$ back into the original equation: $\sqrt{6\times9 - 5}+1=\sqrt{54 - 5}+1=\sqrt{49}+1 = 7 + 1=8$, which matches the right - hand side. So $n = 9$ is a valid solution.

Answer:

9