Real Numbers

A number whose square is non-negative is called a real number.

• Real numbers follow Closure property, associative law, commutative law, the existence of an additive identity, existence of additive inverse for Addition.
• Real numbers follow Closure property, associative law, commutative law, the existence of a multiplicative identity, existence of multiplicative inverse, Distributive laws of multiplication over Addition for Multiplication.

Rationalisation

If we have an irrational number, then the process of converting the denominator to a rational number by multiplying the numerator and denominator by a suitable number is called rationalisation.

Example:

3/√2 = (3/ √2) x (√2/√2) = 3 √2/2

Laws of Radicals

Let a>0 be a real number, and let p and q be rational numbers, then we have:

i) (a^p).a^q = a^(p+q)

ii) (a^p)^q = a^pq

iii)a^p/a^q = a^(p-q)

iv) a^p x b^p = (ab)^p

Example: Simplify (36)^½

Solution: (6²)^½ = 6^{(2 x ½)} = 6¹ = 6