Question

Simplify the expression.

$\sqrt{54t^2}$

Short answer

The simplified value is$3\sqrt{6}t$.

Step-by-step solution

Step 1. Given Information.

The given expression is$\sqrt{54t^2}$.

Step 2. Calculation.

The expression can be simplified as,

$\begin{array}{c}\sqrt{54t^2}={\left(54t^2\right)}^{\frac{1}{2}}\\ ={\left(54\right)}^{\frac{1}{2}}{\left(t^2\right)}^{\frac{1}{2}}\\ ={(2\times 3\times 3\times 3)}^{\frac{1}{2}}{\left(t^2\right)}^{\frac{1}{2}}\\ =3\sqrt{2\times 3}t\end{array}$

On further simplification,

$3\sqrt{2\times 3}t=3\sqrt{6}t$

Step 3. Conclusion.

The simplified value of the given expression is$3\sqrt{6}t$.