Question

write the following expression in simplest form.
\sqrt{3^{2} \cdot 11^{4}}

\sqrt{3^{2} \cdot 11^{4}} = \square
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Use the property of square roots $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$

$\sqrt{3^2 \cdot 11^4}=\sqrt{3^2}\cdot\sqrt{11^4}$

Step2: Simplify each square root. Recall that $\sqrt{x^2}=x$ (for $x\geq0$) and $\sqrt{x^4}=x^2$ (since $(x^2)^2 = x^4$)

$\sqrt{3^2}=3$ and $\sqrt{11^4}=11^2 = 121$

Step3: Multiply the results

$3\times121 = 363$

Answer:

$363$