Surds and Indices

Before solving the numerical on this chapter make sure that you are perfect with the chapter of square and square roots, simplification, linear and quadratic equations and decimal fractions.

Important Terms

Surd: Number which cannot be expressed in the fraction form of two integers is called as surd. Hence, the numbers in the form of √3, ³√2, ……. ⁿ√x

For example: a³ is a number with an index of 3 and base ‘a’. It is called as “a to the power of 3”Irrational numbers which contain the radical sign (√ ) are called as surds.

Indices: Indices refers to the power to which a number is raised. Index is used to show that a number is repeatedly multiplied by itself.

1) The laws of indices and surds are to be remembered to solve problems on surds and indices.

Laws of Indices

Lows of Surds

Important points to Remember

1) Any number raised to the power zero is always equals to one. (Eg: x ⁰ = 1)
2) Surd ⁿ√x can be simplified if factor of x is a perfect square
3) If denominator in a fraction has any surds, then rationalize the denominator by multiplying both numerator and denominator by a conjugate surd.
4) Every surd is an irrational number, but every irrational number is not a surd.
5) The conjugate of (2 + 7i) is (2 – 7i)
6) Different expressions can be simplified by rationalizing the denominator and eliminating the surd.