Find the value of a 5th-root expression. Simplify and find the value of the expression:
$$\sqrt[5]{\frac{123+\sqrt{15125}}{2}}+\sqrt[5]{\frac{123-\sqrt{15125}}{2}}.$$
I tried to rationalise it.
It was of no use..

Let 
$$\sqrt[5]{\frac{123+\sqrt{15125}}{2}}+\sqrt[5]{\frac{123-\sqrt{15125}}{2}}=x$$
Raise to the power of 5 on both sides,
$$(\sqrt[5]{\frac{123+\sqrt{15125}}{2}}+\sqrt[5]{\frac{123-\sqrt{15125}}{2}})^5=x^5$$
Use the identity:
$$(a+b)^5=a^5+b^5+5ab[(a+b)^3-ab(a+b)]$$
We know that $(a+b)=x$.
Simlifying $a×b$ that is 
$\sqrt[5]{\frac{123+\sqrt{15125}}{2}}×\sqrt[5]{\frac{123-\sqrt{15125}}{2}},$ we get $1$.
By substituting, the expression simplifies to the polynomial $$x^5=123+5[x^3-x]$$
$$x^5-5x^3+5x-123=0$$
Solving the degree 5 polynomial, we get
$$x=3$$..$Ans..$
