Question

simplify the radical expression.\\(\sqrt{484x^{18}}\\)\
write your answer in the form \\(a\\), \\(\sqrt{b}\\), or \\(a\sqrt{b}\\), where \\(a\\) and \\(b\\) are constants or expressions in \\(x\\). use at most one radical in your answer, and at most one absolute value symbol in your expression for \\(a\\).

Explanation:

Step1: Factor the constant term

$484 = 22^2$

Step2: Rewrite the radical as product

$\sqrt{22^2 \cdot x^{18}}$

Step3: Split radical into product of radicals

$\sqrt{22^2} \cdot \sqrt{x^{18}}$

Step4: Simplify each radical

$\sqrt{22^2}=22$, $\sqrt{x^{18}}=x^9$ (since $x^{18}=(x^9)^2$)

Step5: Multiply the simplified terms

$22 \cdot x^9$

Answer:

$22x^9$