121. Find the value of the difference

$$
A=\sqrt{|12 \sqrt{5}-29|}-\sqrt{12 \sqrt{5}+29}
$$
S o l u t i o n. Noting that $|12 \sqrt{5}-29|=29-12 \sqrt{5}$, we get:

$$
A=\sqrt{29-12 \sqrt{5}}-\sqrt{29+12 \sqrt{5}}
$$

Since

$$
29-12 \sqrt{5}=20-12 \sqrt{5}+9=(2 \sqrt{5}-3)^{2}
$$

and $29+12 \sqrt{5}=(2 \sqrt{5}+3)^{2}$, we obtain that

$$
A=2 \sqrt{5}-3-(2 \sqrt{5}+3)=-6
$$

A n s w e r: -6 .