Question

simplify the radical expression.\\(sqrt3{1000x^{3}}\\)\
write your answer in the form \\(a\\), \\(sqrt3{b}\\), or \\(asqrt3{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 radicand

$\sqrt[3]{1000x^3} = \sqrt[3]{10^3 \cdot x^3}$

Step2: Apply cube root property

$\sqrt[3]{10^3 \cdot x^3} = \sqrt[3]{(10x)^3}$

Step3: Simplify the cube root

$\sqrt[3]{(10x)^3} = 10x$

Answer:

$10x$