# cube

## DIY Problems for the MIDDLE SCHOOL

The tasks of this set require you to get down to some actual cut and paste work. Arm yourself with a chart paper, a roll of cello tape and a pair of scissors.

## 'CuRe' TRIPLETS

O n observing the triple (25, 125, 225) in which 125 is a perfect cube, 25 and 225 are perfect squares, and the three numbers are in arithmetic progression (AP), I felt that 125 is a very special perfect cube which is guarded by two perfect squares on either side at equal distance.

A surprising discovery we make is that 125 is guarded by two perfect squares in another way, namely: (81, 125, 169); here, 81 and 169 are perfect squares, and the three numbers are in AP as earlier.

## Two Striking Number Patterns

Sums of squares of the natural numbers from the Pascal triangle.

## Shapes with Sutli: The String Game

This article describes an activity where students created different geometrical shapes using a closed-loop string and developed conceptual understanding by engaging with properties of the shapes. The activity encouraged them to think deeply about the meaning of points, straight lines, edges, faces, and angles of geometrical shapes. Using standard models which are generally available, students only get to view geometrical shapes or build them by following a set of instructions.

## Problems for the SENIOR SCHOOL

Here are aset of problems for the senior graders.

## The Digital Root

The concept of digital root of a natural number has been known for some time. Before the development of computer devices, the idea was used by accountants to check their results. We will examine the basis for this procedure presently.

## Practice Questions on Squares and Cubes

Let your learners figure out the questions and solutions to the worksheet that covers squares, cubes and their roots.

1.   Make a question on square root by using following information.

a.   196 sq ft

Make some beautiful cubes from beads this weekend. Easy? Are you ready for the 4 challenges at the end of the activity?

## Understanding the Formulas

In the accompanying article Approximating Square Roots and Cube Roots, the author Ali Ibrahim Hussen has proposed
easy to use formulas for finding approximate values of the square root and cube root of an arbitrary positive number n. The formulas are found to give fairly satisfactory results, as measured by the low percentage error. In this article we explain mathematically why this is so.

## Approximating square roots and cube roots

The idea of equivalent geometric forms is used in this study to devise simple formulas to estimate the square root and the cube root of an arbitrary positive number. The resulting formulas are easy to use and they don’t take much time to calculate.

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