Question

Solve the quadratic equation using square root property.

${\left(t-\frac{5}{6}\right)}^2=\frac{11}{25}$

Short answer

The solutions are$t=\frac{5}{6}\pm \frac{\sqrt{11}}{5}$.

Step-by-step solution

Given Information.   

The Given equation is${\left(t-\frac{5}{6}\right)}^2=\frac{11}{25}$.

Use square root property. 

$t-\frac{5}{6}=\sqrt{\frac{11}{25}}$

Solve radical.

$$\begin{gathered} t-\frac{5}{6}=\pm \sqrt{\frac{11}{5\times 5}} \\ t-\frac{5}{6}=\pm \frac{\sqrt{11}}{5} \end{gathered}$$

Solve for t.

$t=\frac{5}{6}\pm \frac{\sqrt{11}}{5}$

The solutions are$t=\frac{5}{6}\pm \frac{\sqrt{11}}{5}$.