Under certain conditions infinitely nested square roots such as  represent rational numbers. This rational number can be found by realizing that "x" also appears under the radical sign, which gives the equation  If we solve this equation, we find that "x" = 2 (the second solution "x" = −1 doesn't apply, under the convention that the positive square root is meant). This approach can also be used to show that generally, if "n" > 0, then  and is the positive root of the equation "x"2 − "x" − "n" = 0. For "n" = 1, this root is the golden ratio φ, approximately equal to 1.618. The same procedure also works to obtain, if "n" > 1,  which is the positive root of the equation "x"2 + "x" − "n" = 0. Ramanujan posed the following problem to the "Journal of Indian Mathematical Society":  This can be solved by noting a more general formulation:  Setting this to "F"("x") and squaring both sides gives us  which can be simplified to  It can then be shown that  So, setting "a" = 0, "n" = 1, and "x" = 2, we have  Ramanujan stated the following infinite radical denesting in his lost notebook: The repeating pattern of the signs is formula_70  Viète's formula for , the ratio of a circle's circumference to its diameter, is  In certain cases, infinitely nested cube roots such as  can represent rational numbers as well. Again, by realizing that the whole expression appears inside itself, we are left with the equation  If we solve this equation, we find that "x" = 2. More generally, we find that  is the positive real root of the equation "x"3 − "x" − "n" = 0 for all "n" > 0. For "n" = 1, this root is the plastic number "ρ", approximately equal to 1.3247. The same procedure also works to get  as the real root of the equation "x"3 + "x" − "n" = 0 for all "n" > 1. An infinitely nested radical formula_76 (where all formula_77 are nonnegative) converges if and only if there is some formula_78 such that formula_79 for all formula_80.