An interdisciplinary connection in the school learning process is a necessary condition for successful teaching. Properly executed drawing of geometric shapes according to the rules of rectangular projection is one of the solutions of mathematical problems in geometry. Such ways of construction as the replacement of the projection planes, rotation and alignment demonstrate finding out of an actual size of a segment and a plane.

In the paper, we consider some fractional and irrational expressions, and prove the assertion that leads them to fractional and rational expressions, and also consider one general lower and upper bound (two-sided estimate) for a one numerical series. In obtaining some congruencies, we used the formula for binomial coefficients, then from the sum of the left side we cancel each other, and the summons with even numbers, where everywhere in an even degree in an uneven degree are doubled even after multiplier was put outside, all the summons remain free from the square root. Several variants of proofs are considered in the solution of certain problems and theorems.