Question

Solve a quadratic equation by the square root method and write the solution in radical form simplify the solutions

Answer 1

The quadratic equation is given to be:

`3x^2=36`

Divide both sides by 3:

`\begin{gathered} x^2=(36)/(3) \\ x^2=12 \end{gathered}`

Recall the rule:

`\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=√(f\left(a\right)),\:\:-√(f\left(a\right))`

Therefore, we have that:

`x=\pm√(12)`

Simplifying the radical, we have:

`√(12)=√(4\cdot3)=2√(3)`

Therefore, the solution is:

`x=2√(3)\text{ or }-2√(3)`