This library is built in the open.
If you spot an error, have a suggestion, or just want to say hello — we’d love to hear from you.

This verse completes the traditional Indian algorithm for cube root extraction. It is a step-by-step numerical process similar to long division, but based on the algebraic expansion of $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$.
Example.
The calculation for finding the roots of the previously mentioned cubes:
1, 8, 27, 64, 125, 216, 343, 512, 729, 1,728, 46,656, 474,552, 130,323,843.
The resulting cube roots, in order, are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 36, 78, 507.
The "eight operations" (parikarma: basic mathematical procedures) are addition, subtraction, multiplication, division, square, square root, cube, and cube root.
In this section, we first discuss the reduction of fractions to a common denominator. Specifically, the rule for the "class of simple fractions" and related types:
Multiply the numerator and denominator of one fraction by the
denominator of the other; this produces common denominators.
For a whole number, the denominator is understood to be one.
In the case of a "fraction of a fraction," the product of the
denominators is the new denominator, and the product of the
numerators is the new numerator. ॥ 26 ॥
This rule explains how to find a common denominator (samaccheda: "equal divisor") for addition or comparison. It also identifies that any integer is a fraction with 1 as its base.
When adding or subtracting a fraction from a whole number,
multiply the whole number by the denominator and then add
or subtract the numerator.
For complex chains of fractions, multiply the denominators
together and adjust the numerators by their respective
increases or decreases. ॥ 27 ॥
This verse describes how to handle "mixed numbers" and what we now call "compound fractions" (fractions of fractions).
What are the common denominators for the fractions having two, eight, and twelve as their divisors?
How are the following reduced to a common denominator: two-thirds, three-fifths, and the whole number five? ॥ 5 ॥