Surds And Indices

Quick Tips and Tricks

Laws of Surds

2) Expressing a number in radical form

Example: π x ^(m/n) π = ⁿ√ x^m
The exponential form π x ^(m/n) π is expressed in radical form as ⁿ√x^m

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.
• 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.

Rationalizing the denominator:

To rationalize the denominator √ 7 multiply with its conjugate to both numerator and denominator