$${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4\,000}}}}$$
To simplify $${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4\,000}}}}$$ in exact form:
1. Break $${\mathtt{4\,000}}$$ into its simpliest multiples: $${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{5}}}}$$
2. How many of the same number under the radical do you have?: Five $${\mathtt{2}}$$'s, Three $${\mathtt{5}}$$'s
3. Wherever you see three of the same number pull those two numbers out: $${\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}}}$$
4. Multiply the remaining numbers under the radical and numbers ouside the radicall: $${\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4}}}}$$
$${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4\,000}}}}$$ simplified in exact form is $${\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4}}}}$$
In its approximate form: $${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4\,000}}}} = {\mathtt{15.874\: \!010\: \!519\: \!681\: \!994\: \!7}}$$...
.$${\sqrt[{{\mathtt{3}}}]{{\mathtt{4\,000}}}} = {\mathtt{15.874\: \!010\: \!519\: \!681\: \!994\: \!7}}$$
.$${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4\,000}}}}$$
To simplify $${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4\,000}}}}$$ in exact form:
1. Break $${\mathtt{4\,000}}$$ into its simpliest multiples: $${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{5}}}}$$
2. How many of the same number under the radical do you have?: Five $${\mathtt{2}}$$'s, Three $${\mathtt{5}}$$'s
3. Wherever you see three of the same number pull those two numbers out: $${\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{2}}}}$$
4. Multiply the remaining numbers under the radical and numbers ouside the radicall: $${\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4}}}}$$
$${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4\,000}}}}$$ simplified in exact form is $${\mathtt{10}}{\mathtt{\,\times\,}}{\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4}}}}$$
In its approximate form: $${\sqrt[{{\mathtt{{\mathtt{3}}}}}]{{\mathtt{4\,000}}}} = {\mathtt{15.874\: \!010\: \!519\: \!681\: \!994\: \!7}}$$...
