Algebra of Bhaskara II

The sign of Equality (=):

This = sign is called "equal." When this sign is between two terms, it indicates that both are equal to each other.

For example, y = k means that the number represented by y is equal to the number represented by k.

Similarly, y + k = y + n and y + k + n = y + p + l, etc.

Power, Exponent (Power index):

If a quantity is multiplied by itself many times, the product is called the power of that quantity. For example, y × y, y × y × y, y × y × y × y, etc.

Here, y × y is called the square or the second power of y. Therefore, Bhāskarācārya has written "An equal multiplication is called a square kṛti."

Similarly, y × y × y is called the cube (third power), y × y × y × y is called the fourth power, y × y × y × y × y is called the fifth power, and so on.

Roots:

Modern mathematicians use the sign ∛ or for convenience √ to indicate the square root.

For example, ∛y² or √y² indicates the square root of y.

Similarly, the sign for the cube root is ∛. Thus, ∛y³ indicates the cube root of y. In the same way, the signs for the fourth root, fifth root, etc., (∜, ∵) should be used.

Brackets:

These signs ( ), { }, [ ] are called brackets. When an algebraic term is placed between brackets, it should be considered as a single quantity.

For example, (y + k)n means that both y and k are to be multiplied by n. If the expression were y + kn, it would mean that k is to be multiplied by n, and then y is to be added to the product.

Thus, if there is a quantity like (y + k)n + p, here two terms must be assumed: one is (y + k)n and the second is p.

Similarly, n - { p + (y + k)y } should also be considered a binomial, in which the first term is n and the second is { p + (y + k)y }. In the same way, one should understand others elsewhere.