$${\frac{{\left|{\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\sqrt[{{\mathtt{{\mathtt{11}}}}}]{-{\mathtt{177\,147}}}}\right|}}{\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\sqrt{{\mathtt{5}}}}\right)}}$$
11√[-177147 ] = -3 .... so we have
l 5 - 3 l / [2 + √5 ] =
2 / [2 + √5 ] rationalizing the denominator, we have
2 [2 - √5 ] / [ - 1 ] =
2√5 - 4 =
about . 472
I get 0.47.
I don't know if I could have determined the 11th root without a calculator.