After completion of this chapter, students will be able to:

  • find the HCF and LCM of almost three algebraic expressions by the factorization method.
  • simplify the expressions involving radical and surds.
  • simplify the exponential expression and solve the exponential equations.
  • solve the radical algebraic equations.
  • simplify the problems involving algebraic fractions.
  • solve the word problems of linear simultaneous equations and quadratic equations.


Highest Common Factor and Lowest Common Factor Multiple

The Highest Common Factor (H.C.F) of two or more numbers is the largest number that divides evenly into both numbers. In other words, the H.C.F is the largest of all the common factors.The Lowest Common Multiple (L.C.M) is the smallest number that is a common multiple of two or more numbers.


The index of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number.

Roots and Surds

Surds are numerical expressions containing an irrational number. Surds may be quadratic, bi-quadratic, cubic etc. Pure, Mixed, Simple, Compound, Like and Unlike surds are type of surds.

Rationalization and Simplification of algebraic fraction

To rationalize the denominator of a binomial form, we multiply and divide the given binomial irrational number by the conjugate the irrational number in the denominator of the given expression.An equation in which unknown quantity occurs under the rational or root sign is called radical equation. To solve the radical equations, different method are used. But the usual method is to eliminate the radicals by the process of "squaring both sides" and then solving the resulting equation.

Simultaneous Linear Equation in Two Variables

If the pair of values of two variables involved in a pair of equations satisfies both the equations, those equations are called linear simultaneous equation. The method of obtaining the value of the two variables (order pairs) which satisfy both the equation is known as 'solution of equations'.

Quadratic equation

An equation like ax2+ bx + c = 0 where a≠ 0, which contains only one variable and '2' as its highest power is called a quadratic equation. There are two values of the variable in any quadratic equation.