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Surds

Definition

When the square root of a number is the only exact way of writing down the number, it is called a surd.

So square_root_02 is called a surd.

Simplifying Surds

a. Adding and subtracting

Rule: We can add or subtract the square roots of the same numbers only.

b. Multiplying and dividing

Rule: We can multiply and divide surds.

We must be aware of this when multiplying or dividing surds by integers.

Changing the Form of a Surd

		= = x = 2 x = 2
So		= 2

If one of the factors of the number inside the square root is a square number, then it can be square rooted and taken outside.

= 3

Problems

Example 1: A rectangle has a length of (2 + squareroot_3large

) cm and width (3 – squareroot_3large

) cm. Work out the area of the rectangle.

	Area = (2 + ) (3 – ) = 6 – 2 +3 – 3
	Area = (3 + 3 ) cm

Example 2: Simplify x	=
	= x = = 2

Rationalising the Denominator

This is a way of removing the surd from the denominator.

Example 1:

Rule: To rationalise the denominator, multiply above and below by the surd.

Example 2: When the denominator is an expression:

		=		x		=
		=		=

Rule: Multiply above and below by the expression with the sign of the surd changed. This eliminates the surd from the denominator.